But Sunday on "Meet the Press", Giuliani told Chuck Todd that Trump's team has "pretty much decided" that it won't sit down with Mueller, unless the special counsel can prove that there's "some basis for this investigation".
A day after he tweeted "I will always protect my POTUS" in April, the FBI raided his home, office and hotel room as part of a probe by federal prosecutors in NY into his business dealings.
In an earlier interview with ABC News's George Stephanopolous, Cohen said his primary loyalty was to his family and to the United States, a notable change from earlier statements that indicated he would protect Trump above all others.
Giuliani says he has advised Trump that there should be "no discussion of pardons", adding that is "something you can decide down the road".
"There is no evidence of wrongdoing with President Trump".
Giuliani also discussed whether Mr. Trump's Supreme Court nominee should be involved with the Mueller investigation and Mr. Trump's upcoming meeting with Russian President Vladimir Putin. But any testimony would come before Cohen's decision to cooperate, and would be too late to implicate the president, he said.
"It cast a taint over the entire investigation", Mr. Giuliani said on ABC.
Russian Federation summit is a good move
They are not supposed to be building ballistic missiles at an intermediate range but they are and we know they are. Some U.S. officials expressed their concern about a meeting without any other aides present.
Sacha Baron Cohen Gets Dick Cheney to Sign 'Waterboard Kit'
The first episode of Who Is America? premieres July 15 at midnight ET online and later on TV at 10 p.m. ET, with subsequent episodes following each Sunday at 10 p.m.
Starbucks Sippy Cups Will Replace Plastic Straws by 2020
Ice-blended Frappuccinos , meanwhile, will be served with straws made of paper or compostable plastic. Starbucks has designed, developed and manufactured an alternative their calling a strawless lid.
The special counsel is investigating Russian meddling in the 2016 election, whether Mr. Trump's campaign colluded with the Kremlin and whether Mr. Trump obstructed justice in his subsequent actions. "They have to give us factual basis leading to some suspicion of a crime".
On Sunday, Giuliani repeatedly downplayed the possibility that Cohen, who was known for years as Trump's fixer, and who is on tape making threats on behalf of Trump, could provide information to prosecutors that would put the president in any legal jeopardy.
"We've been through everything on collusion and obstruction", he said.
Joe Scarborough laced into Trump attorney Rudy Giuliani on Monday's "Morning Joe" in a rant that included a lengthy list of some of his clients' biggest scandals.
"It's our firm belief, and we think nothing contradicts this, the president did nothing wrong", he said. It was the first in a series of conversations that Comey documented in writing, something Trump lawyers say he did with the ultimate goal of harming the president.
"The fact that the polls are moving away from Mueller is telling", McCarthy said.
Vanity Fair has described Cohen's hiring of Lanny Davis as another move toward Cohen turning evidence against Trump to remain free, noting that the new rumors are of a crowdfunding account coming soon to cover his legal fees.