Appearing on ABC's This Week Sunday, Giuliani said Trump isn't planning to pardon himself, but is likely afforded the ability to under the U.S. Constitution.
"He has no intention of pardoning himself," Giuliani said. "It would be an open question. I think it would probably get answered by gosh, that's what the Constitution says, and if you want to change it, change it."
Giuliani told NBC's Meet the Press the idea of Trump pardoning himself would be "unthinkable" and would likely lead to him being impeached.
"I would think the presidential power, there's nothing that limits the presidential power of pardon from a federal crime, not a state crime," he said. "President Trump is not going to do that. He's obviously not going to give up any of his pardon powers, or any future president's pardon powers, but under these circumstances he's not going to do that."
Giuliani's comments came in response to a 20-page confidential letter to Mueller by Trump attorney Jay Sekulow and then-Trump lawyer John Dowd published by The New York Times, in which they it was impossible for Trump to have committed obstruction in the Russia investigation.
"It remains our position that the President's actions here, by virtue of his position as the chief law enforcement officer, could neither constitutionally nor legally constitute obstruction because that would amount to him obstructing himself, and that he could, if he wished, terminate the inquiry, or even exercise his power to pardon if he so desired," they wrote.
House Republican Leader Kevin McCarthy also denied that Trump had plans to pardon himself and said he would reject the idea of him doing so.
"The president is not saying he is going to pardon himself. The president never said he pardoned himself," he said on CNN's State of the Union. "I don't think a president should pardon themselves."
Former U.S. Attorney Preet Bharara also told State of the Union it would be "outrageous" for Trump to pardon himself.
"I think if the president decided he was going to pardon himself, I think that's almost self-executing impeachment," he said. "Whether or not there is a minor legal argument that some law professor somewhere in a legal journal can make that the president can pardon, that's not what the framers could have intended. That's not what the American people, I think, would be able to stand for."