The interview came on the heels of quite an interesting week for the former mayor of NY.
Giuliani also suggested that Trump wouldn't necessarily comply with a subpoena from Mueller, whose investigation Trump has repeatedly labeled a "witch hunt".
"Why wouldn't you say, "Go in, talk to Robert Mueller, tell the truth"?"
Asked whether Trump could plead the Fifth Amendment, his constitutionally guaranteed right to decline answering questions which might incriminate him, Giuliani said he couldn't be sure.
"I firmly believe there is going to be too much evidence of wrongdoing by him and those around him for him to be able to survive the balance of his term", Avenatti said.
"The president had effectively an extramarital affair slush fund that was administered by Michael Cohen, and that he would just be expected to take care of these things; they were a regular occurrence", Avenatti said.
During a 2016 campaign rally, Trump disparaged staffers of his Democratic opponent, Hillary Clinton, for taking the Fifth during a congressional investigation into Clinton's use of a private email server as secretary of state.
"The reality is, those are not facts that worry me as a lawyer. those don't amount to anything, what's said to the press", Giuliani said.
President Donald Trump's new attorney won't rule out the possibility that the president would assert his Fifth Amendment right against self-incrimination in the swirling Russian Federation investigation.
'I would love to speak, but I have to find that we're going to be treated fairly, ' Trump said at the White House.
Legal experts have said Giuliani's remarks in recent days may have exposed Trump to potential legal risks and could have compromised his attorney-client privilege with the president.
When Trump was asked last month aboard Air Force One if he knew about the payment to Stormy Daniels, he said no. Conway said Trump meant to say he did not know about the payment at the time it was made.
But last week the President said Ms Daniels was paid for "false and extortionist" claims. "It's a nuisance payment", Giuliani continued. She has also filed defamation suits against Trump and his personal lawyer, Michael Cohen, who paid her the money.
"I can't prove that".
The payment has raised questions about whether it violated any campaign finance laws.
Conway also said she did not know of any other payments made to women during the campaign that were similar to the Daniels transaction, saying "they didn't cross my desk as campaign manager".
Cohen, who acted as Trump's "fixer", is facing a criminal investigation in NY, and FBI agents raided his home and office several weeks ago seeking records about the Daniels nondisclosure agreement. He also said he didn't know why Mr Cohen had made the payment or where he got the money. "It may have involved the campaign, doesn't matter, and it would've been done under any other circumstances, if there was no campaign".