President Trump's attorney Rudy Giuliani said on ABC News' "This Week" that Trump "probably does" have the power to pardon himself if special counsel Robert Mueller's investigation found him guilty of obstructing justice in the Russia probe.

He's not, but he probably does. He has no intention of pardoning himself, but that doesn't say he can't. That's really interesting constitutional argument: 'Can the president pardon himself? ... It would be an open question.

— said Giuliani, when host George Stephanopoulos asked if Trump has such authority.

The background: The comment follows a Saturday report detailing how Trump's legal team's new strategy is to argue he can't obstruct the Russia investigation because his presidential authority is so broad it makes obstruction impossible.

They also flirted the possibility of a legal fight over if Mueller’s team ordered Trump to answer questions.

Highlights of Giuliani’s round robin on Sunday morning talk shows:

On the White House's apparent shifting explanations on Trump Tower meeting: "This is the reason you don't let the president testify. Our recollection keeps changing, or we're not even asked a question and somebody makes an assumption," he said on "This Week."

Asked on "Meet the Press" if Trump can terminate any federal inquiry: "It could lead to impeachment, if he terminated an investigation of himself." But, Giuliani added there could be a constitutional argument that Trump could.

Former U.S. attorney Preet Bharara quickly followed up on CNN's State of the Union saying: "I think if the president decided he was going to pardon himself, I think it is almost self-executing impeachment. Whether or not there is an argument that is not what the framers could have intended."