Eric Dewayne Lyons pleaded guilty to failing to register or update his registration as a sex offender, in violation of 18 U.S.C. § 2250(a) and 42 U.S.C. §§ 16911 and 16913. Prior to sentencing, Lyons filed a motion seeking credit for his time spent in state custody from August 28, 2012, the date of his federal indictment, until March 11, 2013, the date of his transfer to federal custody. In response, the government asserted that Lyons was in state custody for a pending charge of violating the state sex-offender registration requirements and that the Bureau of Prisons might give him credit for his time spent in state custody if the similar state charge were dismissed. The district court refused to speculate about how the state *660 case might end and declined to decide whether Lyons should be granted credit for his time in state custody. The district court sentenced Lyons to 20 months of imprisonment followed by 15 years of supervised release.

Although Lyons cites the “reasonableness” standard of review, he does not contend that the district court’s sentencing decision was procedurally or substantively unreasonable. See Gall v. United States, 552 U.S. 38, 51, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007). Although Lyons acknowledges that “the Attorney General, through the Bureau of Prisons, must compute the amount of credit after taking custody of the sentenced Federal Defendant and that it is now up to the Attorney General to correctly reflect the amount of credit that should be given to the Appellant in this case,” he apparently concedes that the district court lacked the authority to grant him credit for his time spent in state custody. (Appellant’s Br. 9). See United States v. Wilson, 503 U.S. 329, 333, 112 S.Ct. 1351, 117 L.Ed.2d 593 (1992) (holding that the Attorney General, not the sentencing court, “computes the amount of the credit after the defendant begins his sentence”); United States v. Crozier, 259 F.3d 503, 520 (6th Cir. 2001) (holding that “[cjredit for time served may be awarded only by the Bureau of Prisons” and that “the district court erred in granting the credit itself’). Instead, Lyons asks this court to order the Attorney General, through the Bureau of Prisons, to give him credit for his time spent in state custody and immediately release him. Lyons fails to identify any legal authority allowing this court to do so. If the Bureau of Prisons declines to give him credit, Lyons may obtain judicial review by filing a petition for a writ of habeas corpus under 28 U.S.C. § 2241 after exhausting his administrative remedies. See Setser v. United States, — U.S. —, 132 S.Ct. 1463, 1473, 182 L.Ed.2d 455 (2012).

Moreover, Lyons is not entitled to credit for the time period at issue. A defendant is limited to receiving credit for time “that has not been credited against another sentence.” 18 U.S.C. § 3585(b). “Time which has been credited towards service of a state sentence may not be ‘double counted’ against a federal sentence.” United States v. Lytle, 565 Fed.Appx. 386, 392 (6th Cir.), cert. denied, — U.S. —, 135 S.Ct. 262, — L.Ed.2d—(2014); see Broadwater v. Sanders, 59 Fed.Appx. 112, 114 (6th Cir. 2003) (“Because Broadwater received credit toward his state sentence for the time period in question, he may not receive credit for this time toward his current federal sentence.”). Lyons supplemented the record with the state court judgment for an unrelated vandalism offense, which shows that he received pretrial jail credit for the period from July 26, 2012, to February 18, 2014. That period encompasses the period for which Lyons seeks credit toward his federal sentence.

For the foregoing reasons, we affirm the district court’s judgment.