Trump has not been shy about using his pardon power.
Trump's lawyer, former New York City Mayor Rudy Giuliani, said this week that he had drawn "red lines" for Mueller in talks over a possible interview with the president.
The lawyers also argued the subpoena would be "a considerable burden for the President and his Office", and that "having him testify demeans the Office of the President before the world".
Giuliani's comments come as the White House sharpens its legal and political defenses against the special counsel Russian Federation probe.
"I can't be confident", Giuliani replied.
Trump's "actions here, by virtue of his position as the chief law enforcement officer, could neither constitutionally nor legally constitute obstruction because that would amount to him obstructing himself", Dowd and Sekulow wrote. The subpoena would then be contested.
"I think the political ramifications would be tough", Mr Giuliani told ABC's This Week.
The letter from Trump's team threw a wrench into the discussions until early March, CNN reported.
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More than a dozen members of the special counsel's team have donated nearly exclusively to Democratic candidates, according to Federal Election Commission records; Kevin Corke reports.
The letter also argues that there is no need for the president to sit for an interview, as the lawyers assert the special counsel has all the information he could possibly need.
Shortly thereafter, The New York Times posted what it describes as a confidential twenty-page document from the president's legal team in January, responding to Special Counsel Robert Mueller's questions. Trump also brought up the cost of the investigation in a May 20 tweet that asked, "At what point does this soon to be $20,000,000 Witch Hunt, composed of 13 Angry and Heavily Conflicted Democrats and two people who have worked for Obama for 8 years, STOP!"
The inclusion of pardoning and ending the probe could serve as both a defense that if Trump was indeed obstructing the investigation, he would have ended it long ago. Topics of Mueller's obstruction investigation include the firings of FBI director James Comey and former national security adviser Michael Flynn, as well as Trump's reaction to Attorney General Jeff Sessions' recusal from the Russian Federation investigation.
That's because, as the country's chief law enforcement officer, Trump himself has ultimate control of the Justice Department and executive branch.
The letter revealed on Saturday puts to bed the question of Trump's involvement, but it doesn't erase the previous denials from the record.
"The appointment of the Special Councel [sic] is totally UNCONSTITUTIONAL!" wrote Trump on Twitter.
Giuliani suggested Sunday that, despite the president's broad powers, a theoretical charge of obstruction may be possible in some cases. The response came from Donald Trump Jr. and -- I'm sure -- in consultation with his lawyer.
The letter, which was not independently verified by CNBC, was authored by John Dowd and Jay Sekulow, lawyers that have since departed Trump's legal team.