President Donald Trump's lawyers are pushing back on a report from The New York Times of a potential shakeup within his legal team.

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.

Trump tweet Why does the Mueller team have 13 hardened Democrats, some big Crooked Hillary supporters, and Zero Republicans? Another Dem recently added...does anyone think this is fair? And yet, there is NO COLLUSION!

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."