ORDER AND JUDGMENT *
Bobby R. Baldock Circuit JudgeRelators Anthony Hanlon and Linda Dollar appeal the district court’s dismissal of their qui tam complaint alleging the defendants violated the Anti-Kickback statute (“AKS”), 42 U.S.C. § 1320a-7b, the False Claims Act (“FCA”), 31 U.S.C. § 3729, and Colorado state law, as well as its refusal to allow them to amend their complaint. Exercising jurisdiction under 28 U.S.C. § 1291, we affirm.
I. Background
The relators are employed by Rehabilitation and Nursing Center of the Rockies, which competes with the defendants for health care business in and around Fort Collins. Defendant Poudre Valley Health Care, Inc. is the only hospital in Fort Collins, and, because a three-day hospital stay is a prerequisite for federally funded nursing home treatment, it is the only referral source in the area for “Medicare A” patients. According to the relators, these patients are desirable because the federal government pays for their care. Defendant Columbine Management Services, Inc. owns and operates nursing homes and other health care facilities in the area.
The relators filed the original qui tam complaint under seal. They alleged that the defendants formed a joint venture to operate a nursing home and to coordinate health care referrals to benefit the joint venture at the expense of other health care facilities and the federal government. They further alleged that the defendants “received a minimum of $150,000.00 in 2009 for these referrals” along with “substantial remuneration in other very significant ways.” Aplt. App., Vol. 1 at 19. According to the complaint, the relators received substantially fewer referrals once the joint venture was formed, and the defendants, on average, billed the government more for services than competing facilities in the area did, costing taxpayers more than thirty million dollars over a ten-year period.
The government declined to intervene in the action. After the defendants were served, they filed motions to dismiss. Once those motions were fully briefed, the rela-tors moved to amend the complaint and to join as a party the joint venture, Centre Avenue Health and Rehab Facility. A magistrate judge denied that motion without *789prejudice, and the relators filed a second motion to amend the complaint.
The magistrate judge issued a report and recommendation to grant the defendants’ motions to dismiss and to deny the second motion to amend the complaint. The magistrate judge first determined that there is no private right of action under the AKS, which is a criminal statute. The relators’ contention that they were pursuing FCA claims based on violations of the AKS was unavailing, according to the magistrate judge, because their complaint did not mention the FCA in the context of their AKS claim. Nor did the complaint or the relators’ briefing specify which part or parts of the AKS the defendants allegedly violated. Therefore, the magistrate concluded that the complaint was deficient as to this claim.
The magistrate judge recommended dismissing the FCA claim because the complaint did not allege any specific instances where the defendants violated their contractual or statutory obligations. Nor did the complaint cite any specific requests for payment that the government likely would have denied had it known of the alleged violations. The relators cited no authority to support their contention that the defendants’ efforts at “funneling” patients to the joint venture were illegal, Aplt. App., Vol. 1 at 18, and they failed to provide factual allegations to support their contention that the defendants did not adequately inform patients about their nursing home options. In other words, the complaint specified neither the laws that the relators believed the defendants had violated nor the conduct which allegedly was illegal.1
Finally, the magistrate judge recommended denying the relators’ motion to amend the complaint because even with the additional allegations in the proposed amended complaint they submitted with their motion, they still failed to state a claim upon which relief could be granted.
Relators objected to the report and recommendation by explaining that, due to illness, their counsel submitted the wrong version of the proposed amended complaint with the second motion to amend. With the objection, they submitted a different version of the proposed amended complaint—the one they purportedly intended to file instead. They requested that the district court “refer the matter back to the Magistrate Judge, and allow [them] to petition the Magistrate Judge for leave to amend again,” id., Vol. 5 at 67, stating that the proposed amended complaint submitted with the objection addressed “most, if not all” of the concerns set forth in the report and recommendation, id. at 69. However, this version showed the federal claims had been deleted, leaving only the state-law claim.
The district court overruled the relators’ objection to the report and recommendation, granted the motions to dismiss, and denied the second motion to amend the complaint. The court adopted the magistrate judge’s recommendation that the original complaint failed to state a claim. It also ruled that the version of the proposed amended complaint submitted with the re-lators’ objection to the magistrate judge’s report and recommendation was not properly before the court because the relators had not sought leave to file it. Nonetheless, the court further concluded neither this version nor the one submitted with the second motion to amend stated a claim on which relief may be granted.
*790II. Analysis
The relators raise two issues on appeal. First, they argue the district court erred by concluding that their original complaint failed to state a claim based on either the AKS or the FCA. Second, they ai’gue the court abused its discretion by not allowing them to amend the complaint.
A. Failure to State a Claim
We review de novo the district court’s dismissal of a complaint for failure to state a claim under Federal Rule of Civil Procedure 12(b)(6). Slater v. A.G. Edwards & Sons, Inc., 719 F.3d 1190, 1196 (10th Cir. 2013). “To survive dismissal, ‘a complaint must contain sufficient factual matter, accepted as trae, to state a claim to relief that is plausible on its face.’ ” Cressman v. Thompson, 719 F.3d 1139, 1152-53 (10th Cir. 2013) (quoting Ashcroft v. Iqbal, 556 U.S. 662, 678, 129 S.Ct. 1937, 173 L.Ed.2d 868 (2009)). “The plausibility standard is not akin to a probability requirement, but it asks for more than a sheer possibility that a defendant has acted unlawfully.” Iqbal, 556 U.S. at 678, 129 S.Ct. 1937 (internal quotation marks omitted). Although we take the factual allegations in the complaint as true, we are not bound to accept legal conclusions couched as factual allegations. Id. “[W]here the well-pleaded facts do not permit the court to infer more than the mere possibility of misconduct,” the complaint has failed to show that the pleader is entitled to relief. Id. at 679, 129 S.Ct. 1937.
1. AKS Claim
In the relators’ original complaint, the first claim for relief was based solely on the AKS—the FCA was not mentioned. The relators concede that they cannot pursue a claim based purely on the AKS: “The Anti-Kickback Statute is a criminal statute and the government is charged with prosecuting criminal conduct, but Relators are not pursuing a straight criminal violation of the AKS. Relators are pursuing False Claims Act claims that are false because of violations of the AKS.” Aplt. App., Vol. 4 at 15. In the absence of any mention of the FCA in connection with this claim, however, the relators failed to put the defendants on notice as to the nature of their claim. “A pleading that states a claim for relief must contain ... a short and plain statement of the claim showing that the pleader is entitled to relief.” Fed. R. Civ. P. 8(a)(2). “Rule 8 serves the important purpose of requiring plaintiffs to state their claims intelligibly so as to inform the defendants of the legal claims being asserted.” Mann v. Boatright, 477 F.3d 1140, 1148 (10th Cir. 2007).
Moreover, the relators cite no authority for the proposition that a violation of the AKS constitutes a violation of the FCA. See generally United States ex rel. Conner v. Salina Reg’l Health Ctr., Inc., 543 F.3d 1211, 1223 (10th Cir. 2008) (declining to decide whether violations of the AKS are actionable through the FCA). Although they argue that the Patient Protection and Affordable Care Act of 2010 expressly provides as much, they do not point to any specific provision of it, nor have they cited any case law that supports their position.
Even assuming for the purposes of this appeal that an AKS violation can be the basis for an FCA claim, the relators have failed to specify which provisions of the AKS the defendants allegedly violated or to provide a factual basis supporting such a violation. “[W]e are not bound to accept as true a legal conclusion couched as a factual allegation.” Iqbal, 556 U.S. at 678, 129 S.Ct. 1937 (internal quotation marks omitted). We agree with the magistrate judge’s assessment of the allegations offered to support this claim: “At most, [the relators] have provided allegations describ*791ing conduct which, while potentially anti-competitive, is not necessarily illegal.” Aplt. App., Vol 5 at 16.
2. FCA Claim
The relators 'argue that their original complaint states a claim for violation of the FCA. We conclude their allegations raise no more than speculative right to relief. The allegations that the defendants referred patients to their own facilities in “vastly disproportionate number[s],” Aplt. App., Vol. 1 at 19, and charged more for services than other facilities in the area do not amount to a showing that the relators are entitled to relief. A false certification claim under the FCA requires a showing that the government might not have made a payment had the alleged violation been known. United States ex rel. Lemmon v. Envirocare of Utah, Inc., 614 F.3d 1163, 1170 (10th Cir. 2010). But the relators do not point to a single claim by the defendants which the government would not have paid had it known of any alleged falsity.
The relators have made no showing that the “funneling” they accuse the defendants of was illegal or that any disclosures they made to patients were inadequate. Their reliance on a special advisory bulletin issued by the Office of Inspector General (“OIG”) is misplaced. A release by the OIG explains that “[t]he bulletin offers several examples of suspect contractual arrangements that could provide the basis for law enforcement action” and lists “[c]haracteristics of potentially problematic arrangements.” Aplt. App., Vol. 3 at 24 (emphasis added). However, “a sheer possibility that a defendant has acted unlawfully” is insufficient to withstand a motion to dismiss for failure to state a claim. Iqbal, 556 U.S. at 678, 129 S.Ct. 1937 (“Where a complaint pleads facts that are merely consistent with a defendant’s liability, it stops short of the line between possibility and plausibility of entitlement to relief.” (internal quotation marks omitted)). If the allegations of the complaint “are so general that they encompass a wide swath of conduct, much of it innocent, then the plaintiffs have not nudged their claims across the line from conceivable to plausible.” Khalik v. United Air Lines, 671 F.3d 1188, 1191 (10th Cir. 2012) (internal quotation marks omitted). The relators’ allegations do not rise to the level of a plausible claim for relief; as a result, they have, not stated a claim for relief under the FCA.
B. Proposed Amendments to the Complaint
We generally review for abuse of discretion the district court’s denial of a motion to amend. Albers v. Bd. of Cty. Comm’rs, 771 F.3d 697, 700-01 (10th Cir. 2014). To the extent the court determined that granting the motion would be .futile, however, we review de novo the court’s finding of futility. Cohen v. Longshore, 621 F.3d 1311, 1314 (10th Cir. 2010). “A proposed amendment is futile if the complaint, as amended, would be subject to dismissal.” Jefferson Cty. Sch. Dist. No. R-1 v. Moody’s Inv’r’s Servs., Inc., 175 F.3d 848, 859 (10th Cir. 1999).
The relators contend they did not intend to file the proposed amended complaint they submitted with their second motion to amend; the proposed amended complaint they submitted with their objection the magistrate judge’s report and recommendation- represents their third attempt to amend the complaint. Yet they have not filed a motion to amend their original complaint by replacing it with this version. A district court does not abuse its discretion by denying a request for leave to cure deficiencies in a complaint when a motion for leave to amend is not properly before it. See Calderon v. Kan. Dep’t of Soc. & *792Rehab. Servs., 181 F.3d 1180, 1187 (10th Cir. 1999). Further, even this version suffers from a blatant deficiency—the first and second claims (which are the basis of this appeal) are entirely struck through, indicating they have been deleted. Under these circumstances, to the extent the district court’s denial was based on a finding of futility, we discern no error.
III. Conclusion
The judgment is affirmed.
After examining the briefs and appellate record, this panel has determined unanimously to honor the parties’ request for a decision on the briefs without oral argument. See Fed. R. App. P. 34(f); 10th Cir. R. 34.1(G). The case is therefore submitted without oral argument. This order and judgment is not binding precedent, except under the doctrines of law of the case, res judicata, and collateral estoppel. It may be cited, however, for its persuasive value consistent with Fed. R. App. P. 32.1 and 10th Cir. R. 32.1.
. The magistrate judge also found that the relators lacked standing to pursue their state-law claim because they had not satisfied statutory prerequisites for doing so. The relators do not appeal the dismissal of this claim.