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.

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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."

Mr. Trump's legal team has undergone some staffing shakeups in recent weeks. Sekulow announced in March that Joseph diGenova, a former U.S. attorney, and his wife and legal partner, Victoria Toensing , would be joining the legal team. Then, Mr. Trump's top attorney on the Russia investigation, John Dowd, abruptly resigned. But then Sekulow announced the diGenova and Toensing wouldn't be formally joining the team after all due to "conflicts."

Giuliani said last week he was joining Mr. Trump's legal team to end the Russia investigation.