Previously Trump has denied knowing in advance that the Trump Tower meeting was going to take place, and he has denied that there was any collusion between his campaign and Russian Federation.
"I'm happy to tell Mueller that Trump wasn't at the Trump Tower meeting", Giuliani said. He even retained Bill and Crooked Hillary's lawyer.
Cohen's lawyer, Lanny Davis, declined comment.
The assertion from Mr. Cohen, who is under federal investigation, is potentially important.
"I put family and country first", he added, signaling that he is willing to cooperate with special counsel Robert Mueller and prosecutors from the Southern District of NY, even if it puts President Trump in jeopardy.
Mr Giuliani said yesterday that the remaining tapes would show that Mr Trump did not know...
One Cohen tape that has surfaced reflects him and Trump in a 2016 discussion that appears to concern a woman who claimed to have had an affair with Trump.
'There are then an untold number of other tapes.
Mr Trump, his son, his lawyers and other administration officials have repeatedly said Mr Trump did not know about the meeting until news of it broke in July 2017.
CNN, citing unidentified sources with knowledge of the matter, said Cohen was willing to make that assertion to Special Counsel Robert Mueller, who is investigating whether Trump's presidential campaign had worked with Russian Federation to sway the 2016 USA presidential election.
Lordy, there are tapes-along with a whole new wave of media questions about Donald Trump, his veracity, the break with his former lawyer, and his current lawyer saying "the president is not an idiot".
"We don't see the legal basis for a president obstructing by merely taking an action in firing somebody that he had every right to fire".
Giuliani also taunted Mueller in an interview with Axios published Monday.
The President also attacked Cohen, claiming he is "trying to make up stories" because of his legal trouble.
Trump Jr. told congressional investigators he did not tell his father about the meeting beforehand, according to documents released by the Senate Judiciary Committee.
Trump Jr responded "I love it" when first offered the political "dirt" on Clinton, the Democratic presidential nominee. That he is, as The New York Times put it yesterday, "increasingly living in a world of selected information and bending the truth to his own narrative". And that direct line between Russian interference and the president has never been proved before.
Trump complained that he had returned from a trip Midwest Thursday "only to be greeted with the ridiculous news" that Mueller and his team "cannot find Collusion... so now they are looking at my Tweets (along with 53 million other people)".
And NBC's Ken Dilanian writes: "I may not understand this stuff, but I thought Trump was rich enough that his whole family could fly private".