Giuliani said he would keep an "open mind" about whether Trump would testify under oath in the probe, but added: "I have to just be honest, we are leaning towards not".
Trump lawyers contended in a 20-page letter to Mueller in January, before Giuliani joined the president's legal team, that he cannot be compelled to testify through a subpoena and argued he could not have obstructed justice by firing FBI director James Comey when he was leading the Russian Federation investigation because as president he has unlimited power to terminate the investigation.
"The Department of Justice is a creature of the president", Giuliani said.
But the president's powers are expansive, and many questions remain about how Trump's office could protect him from the special counsel investigation examining whether his campaign coordinated with Russian Federation to interfere with the 2016 presidential election.
If the president were to pardon himself, Trump would be impeached, he said. But in a 20-page memo to Mueller, which was obtained and published by The New York Times on Saturday, Trump's lawyers admitted that Trump himself dictated the statement. Many hit out at the idea of the president abusing the pardon power, while others raged at the perceived double standard employed by his personal attorney.
Former New Jersey Gov. Chris Christie agreed on Sunday, telling "This Week" that there is "no way" Trump will pardon himself. They said that while the courts might ultimately limit what the president could be asked, it was unlikely they would agree with the president's legal interpretation that he cannot obstruct justice.
"I mean, this is the reason you don't let the president testify", he added. How about you get rid of Scott Pruitt's private security force that he has with him at all times, because that's costing us three and a half million dollars every year. Writing in a tweet in July 2017, the president asserted his "complete power to pardon" in response to the investigation into Russia's alleged meddling in the 2016 election.
Critics accused Mr Trump of subverting the rule of law. I spent a moment wondering, but in the end I think they didn't mean this the way it sounds.
The letter is "pretty extraordinary" in that it states an action that would otherwise be illegal isn't illegal when a president does it, former Manhattan federal prosecutor Mimi Rocah said.
"Most likely, a Trump self-pardon would spark a battle between those who believe it's legal, simply because it's not specifically forbidden in the Constitution - and those who believe it's illegal, because it offends traditional legal sensibilities", she writes. "I think people would erupt. Should have told me!"
Both Russia and Mr Trump deny collusion, and the President has denied obstructing the probe.