The letter is dated January 29 and addressed to Mueller from John Dowd, a Trump lawyer who has since resigned.
Numerous Trump campaign associates and other individuals have been interviewed as part of Mueller's investigation.
"I think the political ramifications of that would be tough". "I think a mistake was made".
The former New York City mayor is Trump's lead attorney in the ongoing Russian Federation investigation.
Last week Trump pardoned Dinesh D'Souza, the conservative author convicted of making illegal campaign contributions, and said he might commute the sentence of former Governor Rod R Blagojevich of IL, and pardon lifestyle guru Martha Stewart.More news: Allies' defense chiefs vow support for summit diplomacy on North Korea
"I think if the president decided he was going to pardon himself, I think that's nearly self-executing impeachment", he said.
"This understanding of presidential power is radical and absolutist", he said.
The Justice Department declined to comment on the claims. "You gotta change the dynamic and put the pressure on them", Giuliani said.
He also played down the possibility that Trump could pardon himself, suggesting he might have that authority but would be unwise to use it.
Berkley law professor and former George W. Bush adviser John Yoo says the United States constitution gives the president virtually unlimited pardon power.
In response to questions about Trump's tweet on Monday, Sarah Huckabee Sanders said: "Thankfully, the president hasn't done anything wrong and wouldn't need one". Andrew Wright, a former associate counsel in the Obama White House, said allowing the president to pardon himself would be contrary to fundamental principles of the American legal system. He has already pardoned I Lewis Libby Jr, former aide to Vice President Dick Cheney, and former Arizona sheriff Joe Arpaio. "There is case law that says if you accept a pardon you are admitting you're guilty".
The interview on Monday also touched on how Giuliani, once hailed in many political corners following his leadership during the September 11 attacks, has become a polarizing figure due to his pugnacious and sprawling defense of Trump.