President Trump's lawyer Rudy Giuliani said Sunday that the president's former lawyer, Michael Cohen, "should cooperate" with prosecutors, and that if he tells the truth, Trump has nothing to worry about.

Giuliani made the television rounds Sunday morning, appearing on three different programs, as speculation grew louder last week that Cohen was inching closer to criminal charges and possibly working out a deal with prosecutors.

"Michael Cohen should cooperate with the government," Giuliani said on ABC's This Week.

"So you have no concerns at all about anything that Michael Cohen might tell the prosecutors?" asked ABC host George Stephanopoulos.

" Zero. None," Giuliani said. "As long as he tells the truth, we're home free."

In an interview last week with Stephanopoulos, Cohen acknowledged that he soon could face criminal charges in an ongoing FBI probe of his finances and business dealings. He also signaled a willingness to cooperate with federal prosecutors, even if what he tells them or special counsel Robert Mueller could imperil the president.

"My wife, my daughter and my son have my first loyalty and always will," Cohen said. "I put family and country first."

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.

"There is no evidence of wrongdoing with President Trump. So, we're very comfortable," Giuliani said on CNN's State of the Union. "If [Cohen] believes it's in his best interest to cooperate, God bless him. He should cooperate."

In April, Trump said he did not believe Cohen would cooperate with investigators.

"Most people will flip if the Government lets them out of trouble, even if it means lying or making up stories," Trump tweeted. "Sorry, I don't see Michael doing that despite the horrible Witch Hunt and the dishonest media!"

Giuliani used the interviews to question the integrity of the Mueller probe, which is tasked with investigating Russia's efforts to interfere in the 2016 election, and whether or not the Trump campaign coordinated with Russia.

He said that the president would not agree to be interviewed as part of the Mueller probe unless the special counsel "can satisfy us that there's some basis for this investigation."

"What we're asking them for is: Is this the witch hunt that a lot of people think it is? Or is there a factual basis for this?" Giuliani told NBC's Meet The Press.

Mueller has already filed at least 23 indictments as part of the special counsel probe and five defendants have pleaded guilty, although none of the indictments directly involve wrongdoing by President Trump.

"It's our, it's our firm belief, and we think nothing contradicts this, that the president did nothing wrong," Giuliani said.

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