Attorneys filed the motion Thursday on behalf of the New Jersey Democrat and his co-defendant and friend, Florida eye doctor Salomon Melgen.
Menendez is charged with accepting free flights on a private jet and luxury vacations from Melgen in exchange for using his political influence with executive branch officials. He has repeatedly denied the charges since the indictment was handed up in mid-2015.
After an 11-week trial that began in early September, jurors deliberated for seven days without reaching a verdict before U.S. District Judge William Walls declared a mistrial on Nov. 16. Several jurors said afterward that as many as 10 members of the panel favored acquittal.
The Department of Justice hasn't announced whether it plans to retry the two men. A department spokeswoman didn't immediately return a message seeking comment Friday.
Walls already denied a defense motion for acquittal during the trial, rejecting arguments that the prosecution had failed to show connections between Melgen's gifts and Menendez's actions.
In their letter to Walls on Thursday, defense attorneys wrote that "scrutiny of the evidence remains warranted, especially given the press statements by jurors and alternates about the lack of proof."
Menendez, a former chairman of the Senate Foreign Relations Committee who has been in the Senate since 2006, is up for re-election next year and is expected to run, though he hasn't officially announced his candidacy.
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