"He probably does," he said. "He has no intention of pardoning himself, but he probably - not to say he can't."
The Constitution, in Article II, states that the President "shall have Power to grant Reprieves and Pardons for Offences against the United States."
"I think it would probably get answered by, 'Gosh that's what the Constitution says, if you want to change it, change it.' I think the political ramifications of that would be tough," Giuliani said.
On NBC, Giuliani framed the pardon question as purely hypothetical and politically implausible.
"It's not going to happen. It's a hypothetical point," he told host Chuck Todd. He went on to describe such a move as "unthinkable" and said it would probably lead immediately to impeachment.
This is not the first time the issue of the President's ability to pardon himself has come up. As early as last northern summer, as Mueller's probe proceeded, the President began quietly asking advisers about his power to pardon aides, family members and even himself. His lawyers at the time began discussing his pardoning powers as well.
Giuliani said it remains an open question whether the President will testify in the investigation. He said that Trump wants to testify but that Giuliani and his team are leaning against recommending that.
"This is the President's decision ultimately," he said. "He believes he's telling the truth. He is telling the truth. He believes justice should win out." But, Giuliani added: " I'm a lawyer ... It's not that simple."
Later in the same programme, former Governor Chris Christie, (R), dismissed the argument put forward by the Trump legal team that the President inherently cannot obstruct justice.
"It's an outrageous claim. It's wrong," Christie, a former US Attorney, said. "They were trying to make a broad argument. Lawyers do that all the time in briefs even to court."
Trump engaged in jabs at the Justice Department via Twitter, going so far as to put "Justice" in quotes. The President expressed dismay that, when still a candidate, he wasn't told that authorities were probing Paul Manafort, who was hired as Trump's campaign chairman. Manafort has been charged by Mueller with multiple offences, including money laundering, conspiracy and bank and tax fraud.
"As only one of two people left who could become President, why wouldn't the FBI or Department of 'Justice' have told me that they were secretly investigating Paul Manafort (on charges that were 10 years old and had been previously dropped) during my campaign? Should have told me!" Trump wrote.
He added: "Paul Manafort came into the campaign very late and was with us for a short period of time (he represented Ronald Reagan, Bob Dole & many others over the years), but we should have been told that Comey and the boys were doing a number on him, and he wouldn't have been hired!"