The sources cautioned against presuming the President would sit down with Mueller in the next few weeks, saying there is much to be negotiated still.
One source said the form of the interview is still in preliminary discussion. Trump's attorneys would like the President's answers to come in written form only, but recognize it could end up being more of a combination of written and in-person interviews, or even solely an interview.
The Washington Post
first reported on Mueller's interest in questioning Trump on Tuesday.
The Post, citing two people familiar with Mueller's plans, said the special counsel is seeking to ask Trump about the decisions that led to ousting Flynn as national security adviser in February and Comey as FBI director in May.
The sources told the Post that Trump's legal team has worked out terms it could present to the special counsel "as soon as next week" and that the team hopes to have Trump's testimony only partially through a face-to-face interview, with other answers coming through a written statement.
The report on the potentially imminent questioning of the President came the same day news emerged that Attorney General Jeff Sessions and former FBI Director James Comey have both spoken with special counsel investigators.
One source said told the Post that Mueller has expressed interest in Trump's "efforts to remove" Sessions, and that Mueller is trying to glean if there is a "pattern" of behavior from Trump. The President has publicly rebuked the attorney general, calling
him "beleaguered" last summer. In December, Trump told The New York Times
it was "too bad" Sessions had recused himself from the Russia investigation.
White House press secretary Sarah Sanders said the White House is "fully cooperative" with Mueller but believes the American people are ready to move on.
"Look, as we've said probably just about every day this year since we've been here that we're going to be fully cooperative with the special counsel and we'll continue to do that throughout the process," Sanders told reporters Tuesday.
"We're also not going to comment on who may or may not or could be interviewed at any point," she added. "We're going to continue to be fully cooperative with the process."
Sanders added: "Frankly, this administration, we've said it time and time before, there was no collusion and there's nothing to it. We're ready to move on. Clearly the American people are."
Peter Carr, the Justice Department spokesman for the special counsel probe, declined to comment to the Post as did two attorneys for Trump.
Flynn left the White House in February 2017 amid reports he misled Vice President Mike Pence about his conversations with Sergey Kislyak, who was the Russian ambassador to the US at the time.
shortly after Trump entered office that the US was investigating Flynn's calls with Kislyak.
That news emerged in the wake of Flynn's ouster that Trump had known
for two weeks that the Justice Department was concerned about Flynn's contact with Kislyak, and Flynn did not exit until days after the Post reported
he discussed sanctions with Kislyak, a finding that directly contradicted Pence's prior claim.
Flynn pleaded guilty
in December to lying to the FBI about conversations with Kislyak and disclosed he was cooperating with the Mueller-led probe.
Comey was fired in early May, and soon after his ouster, it became public he had kept contemporaneous memos on meetings with the President, where he said Trump asked him to let go of an investigation into Flynn.
Comey later said he believed he was fired to affect the investigation into potential coordination between Trump's associates and Russia to influence the 2016 election.
Trump denied making the request, and as speculation mounted over whether those conversations and other reported calls from Trump and the White House to influence the Russia investigation constituted obstruction of justice, a lawyer for Trump said late last year the President, by the nature of the office, could not obstruct justice.