Appointing a special master could block the government from continued access to the files until the special master has gone through them and would potentially pave the way for lengthy litigation that could bog down the investigation.

As a matter of substance, the request is puzzling. Mr. Trump’s lawyers made it far too late, so the F.B.I. has already seemingly examined everything. Indeed, on Monday, the Justice Department said it had reviewed documents seized in the search and set aside those possibly covered by attorney-client privilege — a different issue from the one Mr. Trump had raised.

“They’ve already looked at it,” said Barbara L. McQuade, a University of Michigan law professor who was the U.S. attorney for the Eastern District of Michigan from 2010 to 2017. “The horse is out of the barn.”

Moreover, Mr. Trump already tried to assert executive privilege to block the F.B.I. from examining boxes of files the National Archives had earlier retrieved from Mar-a-Lago. That assertion failed after President Biden did not back him and the Justice Department advised the agency that the needs of a criminal investigation can outweigh the privilege.