Trump fired his shot at the special counsel leading the Russian Federation probe in an interview with the Daily Caller, where he resumed claims that conflicts of interest prevent Mueller - who has already won a conviction of Trump's former campaign manager Paul Manafort - of having conflicts of interest.
Mueller will accept written answers from Trump on questions about whether his campaign conspired with Russia's election interference, Mueller's office told the president's lawyers in a letter, two people briefed on it said.
The letter was the latest in lengthy negotiations the two sides have engaged in about whether Trump will be formally interviewed in the investigation.
In an interview with the conservative Daily Caller, President Trump expounds upon his oft-stated theory that Robert Mueller has several conflicts of interest that should prevent him from investigating Trump's web of criminality and misconduct.
Sources said the tone prompted Trump allies to believe that any interview will be more limited in scope than the president's legal team initially believed.
Although the Times reports that Mueller "did not say that he was giving up on an interview altogether".More news: First photos of Brie Larson as Captain Marvel released
'It's incredible when you look at Weissmann and all these people, ' Trump said, bringing up the chief of the criminal fraud section who is working for Mueller.
Special counsel spokesman Peter Carr declined to comment Tuesday.
It was not immediately clear what those conditions mean for other questions Mueller is exploring.
The White House Counsel's Office, led by attorney Emmet Flood, has been girding to fight a subpoena for Trump's testimony under oath.
Mueller's office has been trying to determine the president's state of mind during several episodes as president, including the firing of Comey and his public criticism of Attorney General Jeff Sessions about recusing himself from the Russian Federation investigation. "You know, he's Comey's best friend", said Trump. In other words, they will not allow any questions that go to the issue of obstruction of justice.
And for another, Trump claimed, without any proof that Comey and Mueller are "best friends" and even more, of the "hugging and kissing" variety.