According to ABC News, Giuliani is actually pushing for Trump to interview Mueller and met with Mueller on Tuesday to discuss it:
Here’s more from CBS News:
CBS NEWS – Rudy Giuliani and President Trump’s newly reconfigured legal team met Tuesday with special counsel Robert Mueller and his staff to discuss a possible interview, sources close to the process confirm to CBS News’ Major Garrett. Giuliani last week joined Mr. Trump’s legal team, along with Jane and Marty Raskin, who are former federal prosecutors.
Sources said the probability of a Trump-Mueller interview is now higher than it was in the immediate aftermath of April 9 raids on Michael Cohen’s offices, home and hotel room. The raids on Cohen, who is under criminal investigation, were conducted by the Southern District of New York after a referral by Mueller.
But the raids antagonized Mr. Trump and stalled interview talks, Garrett reports. Giuliani, the former U.S. Attorney of the Southern District of New York, was brought it with the hopes of rekindling those negotiations.
Giuliani appears to be taking the lead role as potential closer on the interview and public face of team, Garrett reports. Jane and Marty Raskin are focusing on the underlying law and preparations for an interview, should it occur, Garret reports.
The news of the meeting between Giuliani and Mueller was first reported by The Washington Post. Jay Sekulow, another member of Mr. Trump’s legal team, told The Washington Post “we don’t discuss conversations with the Office of the Special Counsel.”
As you know, Giuliani has said he will put an end to the Mueller investigation. It sounds like he might be trying to use the interview as leverage to do just that. However, that’s a very risky proposal to sit Trump down in front of Mueller. Nobody with any sense thinks this would be a good idea. In fact most of us think it probably wouldn’t end well for Trump.