The June 27, 2017, letter was written by Marc Kasowitz, then the president's lead lawyer, as Mueller and his team were in the early stages of their investigation into Trump associates and as they had begun examining whether the president, by firing Comey, had sought to stymie an FBI investigation into the Trump campaign's ties to Russian Federation.
Federal Bureau of Investigation agents raided Cohen's home, office and hotel room in NY in April as part of a probe into his business dealings.
However, Giuliani suggested there could have been an "understanding" between Trump and Cohen that he would get repaid $140,000 for things like this "nuisance settlement".
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".
Cohen, 51, has scrubbed any mentions and photos from his Twitter profile that previously identified him as "Personal attorney to President Donald J. Trump" and, in what has been called a "warning shot", hired Lanny Davis, a close friend of Bill and Hillary Clinton, to join his legal team.
Giuliani on Sunday said Mueller's team would first have to demonstrate a "factual basis" for their probes into Russian collusion and obstruction of justice. "If [Cohen] believes it's in his best interest to cooperate, God bless him".
As a result, he claimed, he could confidently say that Trump had nothing to answer. "Sorry, I don't see Michael doing that despite the awful Witch Hunt and the dishonest media!"
Trump lawyer Rudy Giuliani implied to ABC's George Stephanopoulos Sunday that President Donald Trump pressured former FBI Director James Comey to "give the man a break" and drop the investigation into ex-White House national security adviser Michael Flynn. What we're asking them for is: Is this the witch hunt that a lot of people think it is? Mueller doesn't have a "factual basis" for investigating the president.
He also professed to be untroubled by either the prospect of Trump being served with a subpoena to appear before the inquiry, or by his former lawyer, Michael Cohen, flipping and handing over all his information to Mueller.
"We have no reason to believe he did anything wrong", the former New York City mayor said of Cohen.