A spokesman for the special counsel's office, Peter Carr, declined to comment. A White House spokesman referred questions to the President's legal team. Two lawyers for Trump, Jay Sekulow and John Dowd, declined to comment
Within the past two weeks, the Special Counsel's office has indicated to the White House that the two central subjects that investigators wish to discuss with the President are the departures of Flynn and Comey and the events surrounding their firings.
Flynn resigned last February after the Washington Post reported that he misled Vice-President Mike Pence and other Administration officials about his communications with the Russian ambassador to the United States.
Late last year, Flynn pleaded guilty to lying to the FBI about his contacts with the Russian ambassador. Trump then tweeted that "he had to fire General Flynn because he lied to the Vice-President and the FBI." Previously, the White House had cited only the false statements to Pence as a rationale for dismissing Flynn.
Trump fired Comey in May, several days after the then-FBI director told Congress he could not comment on whether there was evidence of collusion between the Trump campaign and Russia. Comey later testified that the President had asked him several months earlier whether he could see a way to "letting Flynn go".
Mueller has also expressed interest in Trump's efforts to remove Jeff Sessions as Attorney-General or pressure him into quitting, according to a person familiar with the probe who said the Special Counsel was seeking to determine whether there was a "pattern" of behaviour by the President.
This month Trump declined to say whether he would grant an interview to Mueller and his team, deflecting questions on the topic by saying there had been "no collusion" between his campaign and Russia during the 2016 presidential election.
"We'll see what happens," Trump said when asked directly about meeting with the Special Counsel.
Behind the scenes, Trump has told his team of lawyers that he is not worried about being interviewed, because he has done nothing wrong, according to people familiar with his views. His lawyers also support a sit-down, as long as there are clear parameters and topics.
However, some of Trump's close advisers and friends fear a face-to-face interview with Mueller could put the President in legal jeopardy. A central worry, they say, is Trump's lack of precision in his speech and his penchant for hyperbole.
People close to Trump have tried to warn him for months that Mueller is a "killer," in the words of one associate, noting that the Special Counsel has shown interest in the President's actions.
Roger Stone, a longtime informal adviser to Trump, said he should try to avoid an interview at all costs, saying agreeing to such a session would be a "suicide mission".
"I find it to be a death wish. Why would you walk into a perjury trap?" Stone said. "The President would be very poorly advised to give Mueller an interview."