Rodriguez admitted in February to using steroids while with the Texas Rangers from 2001-03, but insisted he stopped before he was traded to the Yankees in February 2004.
A team spokesman said the Yankees had no comment.
The development comes just two weeks after federal prosecutors asked an appeals court to stay its decision that government agents illegally seized the drug testing records and samples of more than 100 baseball players.
The move could keep baseball's infamous drug list from being destroyed for at least a few months.
In a filing late Monday with the 9th U.S. Circuit Court of Appeals, the U.S. attorney's office in San Francisco said the Solicitor General, in consultation with the criminal division of the Justice Department and the U.S. attorney's office, was considering whether to ask the Supreme Court to review the decision.
The deadline for a filing with the Supreme Court is Nov. 24.
"There is good cause for a stay," the government wrote in a motion filed by Joseph P. Russoniello, the U.S. attorney in San Francisco, and signed by Barbara J. Valliere, chief of his appellate section.
Prosecutors wrote that if the decision isn't stayed, "the district courts will obtain jurisdiction over this case, and the materials seized pursuant to the warrant and subject to the grand jury subpoena may be destroyed. Destruction of the property may render the issues presented by the government's appeals moot."
The 9th Circuit, in a 9-2 decision last week written by Chief Judge Alex Kozinski, ruled prosecutors had the right only to the records of 10 players named on their original search warrants, executed as part of the Bay Area Laboratory Co-Operative investigation.
Players' association general counsel Michael Weiner, who has been designated to succeed union head Donald Fehr, said Wednesday the union has responded that it will not oppose the stay request.
Federal agents raided the offices of baseball's drug-testing companies in April 2004, seized a spreadsheet containing the drug-testing records of all baseball players, mixed in on a computer with those from other sports and businesses, then obtained additional search warrants.
Prosecutors argued they had a "plain-view" right to the records of all baseball players whom they said tested positive.
The appeals court set new rules for searches of digital evidence, saying the "plain-view" doctrine shouldn't apply.