The New York Times reported Tuesday that Mr Giuliani is allegedly seeking a pre-emptive pardon from Mr Trump. The newspaper cites two unnamed people with knowledge of the discussion.
The anonymous sources said it was no clear who broached the topic first, and it was not immediately clear if Mr Trump would follow through on the request.
There were no immediate details regarding the crimes Mr Giuliani allegedly wants pardoned. Federal prosecutors were investigating him last summer for his involvement in Ukraine business dealings that eventually led to Mr Trump's impeachment.
Mr Giuliani's lawyer told the paper in a statement that he's "not concerned about this investigation, because he didn't do anything wrong and that's been our position from Day 1."
A president can grant a pardon for a crime that has not been charged or convicted yet, though it does not happen often.
The most famous example of a broad, pre-charge pardon occurred when Gerald Ford pardoned Richard Nixon following the latter's resignation.
George Washington also pardoned the conspirators behind the Whiskey Rebellion to prevent them from being tried for treason.
Mr Trump has not shied away from using his presidential pardoning power to help his friends. He has already pardoned his ally Michael Flynn, and commuted the sentence of his friend Roger Stone, who were both charged with lying to federal investigators conducting the Mueller investigation. Mr Stone was convicted and Mr Flynn's case was in limbo due to the coronavirus.