(CNN) President Donald Trump is not angry at his attorney Rudy Giuliani, despite the former New York mayor's contradictory answers in recent interviews about a proposed Trump Tower project in Moscow, sources told CNN Tuesday -- and Giuliani is not going anywhere.

A source familiar with the Trump legal team told CNN on Tuesday, "Rudy's not getting fired."

Giuliani has been the subject of intense scrutiny this week after talking himself into hot water during interviews on Sunday morning news programs. In one interview, Giuliani said Trump had been in talks over the proposed Moscow Trump Tower project throughout the presidential campaign, possibly as late as October or November 2016.

The source said the President and others weren't thrilled about the statement, and Trump asked Giuliani to go out and do cleanup.

Giuliani released a statement on Monday backing off that statement and said his comments were hypothetical.

"My recent statements about discussions during the 2016 campaign between Michael Cohen and then-candidate Donald Trump about a potential Trump Moscow 'project' were hypothetical and not based on conversations I had with the President," Giuliani said in that statement. "My comments did not represent the actual timing or circumstances of any such discussions. The point is that the proposal was in the earliest stage and did not advance beyond a free non-binding letter of intent."

Despite a report Tuesday night, the legal team member said Trump wasn't "apoplectic" about Giuliani's statement and ensuing cleanup. The President likes what Giuliani does for him and thinks he is effective, the team member said.

Another person who spoke to Trump on Tuesday told CNN there was no sense of visible anger at Giuliani, adding that his lawyer, who is one of the more prominent faces on TV defending the President, is one of the few people Trump hasn't been screaming about in the last 48 hours.

The source said Trump seemed content after asking Giuliani to clean up the mess he made, adding that the President likes the obfuscation of it all, and that he showed no sign of wanting to fire the lawyer. But that decision, of course, ultimately rests with Trump.

For his part, Giuliani expressed confidence in his relationship with the President in an interview with CNN's Dana Bash Tuesday afternoon.

"He just wants it clarified. He understands how these things happen. It happens to him all the time," Giuliani told Bash.

He added that he's not worried that special counsel Robert Mueller may ask more questions for Trump and his legal team after Giuliani's statements.

"I have no problem giving him that answer if he wants that answer. I think he implicitly understands that," Giuliani said.