Giuliani also spoke confidently of Mueller's investigation of his predecessor, Trump's former personal lawyer, Michael Cohen, in connection to the president's relationship with and Cohen's payments to adult film star Stormy Daniels.
In recent weeks, Cohen has made a number of moves indicating that he's willing to turn against the president if federal investigators from the Southern District of NY or the FBI want him to.
Giuliani seemed to confirm on ABC's "This Week" Sunday that President Trump actually did ask former FBI Director James Comey to drop the probe into ex-White House national security adviser Michael Flynn despite Trump's previous denials that he said anything of the sort.
But any testimony would come before Cohen's decision to cooperate, and would be too late to implicate the president, he said. "We have - we have no reason to believe he did anything wrong".More news: Thailand Cave Rescue Latest: More Schoolboys Are Saved
"I should correct it, I didn't say they have to prove a crime", Giuliani clarified Sunday on CNN's State of the Union. He said an interview with Mueller could be an "attempt to trap him in perjury".
These sources would not comment on whether Cohen's attorney, Guy Petrillo, has been meeting with prosecutors in NY and referred inquiries about any potential case to Petrillo.
The special counsel investigation was established by Deputy Attorney General Rod Rosenstein to handle the FBI's Russian Federation investigation, which began in 2016, after Mr. Trump fired FBI Director James Comey in May 2017.More news: Syrian army captures main border crossing with Jordan amid progress in Daraa
Politico's Josh Gerstein was the first to point out the discrepancy between Giuliani's comments and Trump's denial.
The new demands by Trump's legal team indicate that it is likely to take a more aggressive and combative stance toward Mueller going forward. "We can't find an incriminating anything", Giuliani replied. Cohen gave an interview to ABC last week in which he signaled he might be willing to cooperate. Kasowitz and Trump lawyer Jay Sekulow did not immediately return messages, and former Trump attorney John Dowd declined to comment.
"One source said to me this is his version of July 4th, which is Independence Day", she continued. Mr. Cohen has denied any wrongdoing.More news: Trump to OPEC: 'Reduce pricing now!'
Giuliani told ABC, "We've been through everything on collusion and obstruction".