U.S. District Judge Daniel Holdermann's ruling involved a surreptitiously recorded conversation between Burris, D-Ill., and Robert Blagojevich on Nov. 13, 2008, The New York Times reported.
Lawyers for both men said they have no objection to turning over the tape to the ethics committee, the Chicago Tribune said. Rob Blagojevich's conversations were recorded surreptitiously during a federal investigation of his brother.
The ethics committee is investigating the circumstances under which the impeached governor named Burris to replace Barack Obama in the U.S. Senate.
Michael Ettinger, representing Rob Blagojevich, said that he and his client would like the public to hear the tape.
"We think it is what it is," said Timothy Wright, Burris's lawyer. "The truth is coming out. We expect it to vindicate the senator."
Rod Blagojevich was ousted from office by the state legislature in January and is under indictment on federal corruption charges.