The president has instead in recent days begun publicly assailing Mr. Mueller, a shift in tone that appears to be born of the president's concern that the investigation is bearing down on him more directly.
On Thursday, the president reaffirmed his willingness to meet with Mueller, telling reporters following a trade event at the White House: "Yes, I would like to".
The Times reported on Thursday that Dowd's resignation was due in part to his frustration that Trump was not following his legal advice, particularly as it relates to sitting down for an interview with the special counsel.
The Washington Post broke the story and reports that the resignation was a mutual decision.
Meanwhile, Democrats from the House Judiciary Committee warned Trump's comments about the Mueller probe were "threats" specifically targeting the special counsel.
Washington lawyer Joseph diGenova will join the legal team this week, according to attorney Jay Sekulow, who also represents Trump.
Jens David Ohlin, a vice dean at Cornell Law School who's an expert on criminal law, said Trump's legal team consisted of "two camps".
This has led to rumors that the President is planning on firing Mueller.
John Dowd had become increasingly frustrated with Trump's reliance on other legal minds, and with his baiting Mueller on Twitter.
"We will continue our ongoing representation of the president and our cooperation with the Office of Special Counsel", Sekulow said.
On Thursday, top White House lawyer John Dowd resigned after he reportedly grew exhausted of Trump not listening to his legal advice. "I am pleased to announce that, effective 4/9/18, John Bolton will be my new National Security Adviser", Trump said. But he later clarified that he was speaking for himself and not on Mr Trump's behalf.
His hiring was viewed as a signal that Mr Trump's allies would now be more aggressive in public attempts to discredit the Mueller investigation.
Mr Dowd took over the president's legal team last summer.
"I had to fire General Flynn because he lied to the Vice President and the Federal Bureau of Investigation". "Trump hit the roof", one source said.
The tweet led Sen.
Dowd confirmed his departure to multiple media outlets.