Former FBI Director Robert Mueller is negotiating with President Trump's team about interviewing White House staff in the course of his investigation of Russian interference into the 2016 elections, according to a new report.

Mueller, who was named special counsel by the Justice Department after Trump fired then-FBI Director James Comey, has asked already for notes or other contemporaneous documentation of "specific meetings;" he also wants to talk to former White House chief of staff Reince Priebus about Trump's decision to fire Comey.

"That line of questioning will be important as Mr. Mueller continues to investigate whether Mr. Trump obstructed justice in the dismissal of Mr. Comey," according to the New York Times, which reported on the nascent talks. "Mr. Mueller has expressed interest in speaking with other administration officials, including members of the communications team.

"But Mr. Trump's allies are particularly concerned about Mr. Mueller's interest in talking to Mr. Priebus, a former chairman of the Republican National Committee who worked closely with Mr. Trump during the presidential campaign. Mr. Trump's confidants at the White House say Mr. Trump was never fully convinced that Mr. Priebus would be loyal to him."

Trump's decision to fire Comey resulted in the appointment of the special counsel, as Democrats and even some Republicans suggested the president may have attempted to obstruct justice.

The White House initially claimed that Trump fired Comey based on an unsolicited recommendation made by newly-confirmed Deputy Attorney General Rod Rosenstein. Trump contradicted that explanation within days, saying he intended to fire Comey regardless of what Rosenstein thought.

"[W]hen I decided to just do it, I said to myself, I said 'You know, this Russia thing with Trump and Russia is a made up story — it's an excuse by the Democrats for having lost an election that they should have won,'" Trump told NBC. "So everybody was thinking, they should have won the election. This was an excuse for having lost an election."

Comey responded by leaking notes of his meetings with Trump and eventually appearing before Congress to testify that the president asked him to end an investigation into Mike Flynn, Trump's former national security adviser.

"[Trump] then said, 'I hope you can see your way clear to letting this go, to letting Flynn go. He is a good guy. I hope you can let this go,'" Comey told lawmakers in a prepared statement. "I replied only that 'he is a good guy.' (In fact, I had a positive experience dealing with Mike Flynn when he was a colleague as Director of the Defense Intelligence Agency at the beginning of my term at FBI.) I did not say I would 'let this go.'"

Priebus could be a particularly valuable witness for verifying or debunking various claims about the president.

"Shortly after the November election, Mr. Priebus was made chief of staff, and he was involved in the major decisions the president made during the transition and in the first six months of the administration," the New York Times notes. "Mr. Priebus made a point of being in most meetings and tried to be aware of what the president was doing. Mr. Trump fired him last month."