The Orlando Sentinel said the motion was filed Tuesday.
The film star's 2008 conviction and three-year prison sentence for failure to file tax returns and pay federal income taxes were upheld by an appellate court in July. However, he has remained free on bond and his legal team requested a new trial.
A federal judge in Florida last week denied that petition and ordered Snipes to surrender to the U.S. Bureau of Prisons to begin his prison sentence.
The Sentinel said it was not clear where and when Snipes must turn himself in.
Snipes, 48, starred in the "Blade" trilogy, "White Men Can't Jump," "U.S. Marshals" and "To Wong Foo, Thanks for Everything, Julie Newmar."