This week, it was reported that in discussions with Trump's lawyers in March, Mueller threatened to subpoena Trump to appear before a grand jury if he did not voluntarily agree to an interview.
On Thursday, Giuliani said he wanted limits for any Trump interview with Mueller.
During an appearance Wednesday night on Fox News, Giuliani decried the FBI's raid last month of the Manhattan home, office and hotel room of Trump's longtime personal lawyer, Michael Cohen.
"I would love to speak because we've done nothing wrong", Trump said. But lying to prosecutors to hide crimes isn't a setup or a trap; it's obstruction.
Giuliani's explanation foreshadows a likely defense to the May 2017 dismissal, but it was the latest in a series of rationales offered by Trump and his advisers.
But several experts pointed out an undisclosed campaign loan is also a violation of federal election law.
For, after nearly two years, their Russiagate investigation has produced no conclusive proof of the foundational charge - that Trump's team colluded with Vladimir Putin's Russian Federation to hack and thieve the emails of the Clinton campaign and DNC.
He said Mr. Trump would want to be treated like former Secretary of State Hillary Clinton was when she was the object of an investigation, but "Mueller rejected written answers". Should Trump be removed as a result of such a campaign, the result would be to shift the political system even further to the right.
Trump went on to explain that his lawyers have cautioned against speaking to Mueller, but he said he would override them if he was convinced he'd get a fair hearing.
The New York Times reported in January that McGahn threatened to resign a year ago when Trump ordered Mueller to be fired.
But if the loudest voices come down heavily against the man once admired for his leadership as "America's Mayor" in the aftermath of the September 11, 2001 attacks, others have urged caution.
"In all fairness, Bob Mueller worked for Obama for eight years", he added. "If you look at Mr Giuliani's career he has a lot of relevant high-level experience", a former Manhattan federal prosecutor told AFP.
"It is hardly an improvement to claim that what was claimed as a gift is now a secret loan from your lawyer to pay hush money to a porn star", said Jonathan Turley, a George Washington University Law School Professor who has frequently expressed skepticism about the legal case against the president. He likes to kind of walk into a situation and blow it up.
Neither is he only a lawyer. "But it will furnish mountains of ammunition for combatants on all sides". Perhaps that's all Trump and his team are up to here. If a president commits a crime, the Constitution's scheme, Mr. Giuliani said, is for him to be removed from office and/or prosecuted afterward. Giuliani also once served as US attorney for the Southern District of NY, overseeing federal law enforcement agents, before he became New York's mayor. What is alleged to have been said or done during that meeting remains unclear. "I could not be more happy".