As Trump adds to his legal team in special counsel Robert Mueller's probe of potential links between the Trump campaign and Russia, the Times reported that the status of his lawyers has grown precarious. The Washington Post also reported on potential changes in the president's representation.
John Dowd, the president's lead lawyer in the probe, has considered resigning over Trump's uncontrollable behavior, the Times reported, citing two people briefed on the matter.
But Dowd told CNBC in an email Tuesday that the legal team remains intact. "Delighted Joe is joining," he said, referring to former U.S. Attorney Joseph diGenova, a regular Fox News guest whom Trump added to his team on Monday.
In response to questions about whether Trump will make changes to the team Tuesday as rumored, a source familiar with the situation told CNBC: "No."
The team, the source said, "is fully engaged" — including Dowd and White House lawyer Ty Cobb.
The Times, citing two people briefed on the matter, reported that Trump himself has openly discussed with colleagues the possibility of firing Cobb.
Reportedly shirking the advice of his legal advisors, Trump has taken a pugilistic public stance against the special counsel. Over the weekend, Trump criticized Mueller by name for the first time on Twitter.
Cobb, who previously predicted a speedy end to Mueller's probe of potential links between the Trump campaign and Russia, has reportedly encouraged Trump to cooperate with investigators.
Cobb did not comment on the recent reports about the legal team.
DiGenova told Fox News in January that the government agencies investigating Trump had fabricated evidence against the president in a conspiracy to exonerate Hillary Clinton. Two decades ago, in an op-ed for The Wall Street Journal, diGenova argued that the U.S. "could conceivably benefit from the indictment of a president."
The Washington Post reported on Tuesday that Trump is seeking to add Theodore Olson, a veteran litigator who served in George W. Bush's administration as solicitor general, to the legal team. The Post cited people familiar with the matter.
Olson had previously turned down an offer to join the team, the newspaper said. Olson told the Post he would not comment on this subject, and did not immediately respond to CNBC's request for comment.
However, a partner at Olson's law firm tweeted Tuesday that neither Olson nor the firm, Gibson Dunn, would be representing the president.
Asked by CNBC about changes to the legal team, a White House official who declined to be named said: "We have nothing to announce."
The official added that, eventually, the Russia investigation will end and the lawyers working on it will no longer be needed.
"At some point, Ty Cobb will not have a role here," the official said. "But that does not mean there are changes planned."
-- CNBC's Eamon Javers contributed to this report.