UPDATE: The Washington Post follows up on earlier reporting with more information about the meeting between Mueller and Trump's lawyers late last month and the possibility that an interview could take place sooner rather than later:
Mueller brought up the issue of interviewing Trump during a late December meeting with the president’s lawyers, John Dowd and Jay Sekulow. Mueller deputy James Quarles, who oversees the White House portion of the special counsel investigation, also attended.
The special counsel’s team could interview Trump very soon on some limited portion of questions — possibly within the next several weeks, according to a person close to the president who was granted anonymity to describe internal conversations.
“This is moving faster than anyone really realizes,” the person said, who said Trump is comfortable participating in an interview and believes it would put to rest questions about whether his campaign coordinated with Russia in the 2016 election.
Mueller indicates he will likely seek interview with Trump (WaPo)
NBC News first reported – and CBS News has confirmed – that Special Counsel Robert Mueller's team has started discussions with President Trump's legal team as to how an interview with the president might happen.
The discussions have involved, for example, whether the interview can be written questioning as opposed to in-person questioning. Mr. Trump's lawyers had met with Mueller and his team on Dec. 22, according to two sources with direct knowledge.
While this stage in the process is early and preliminary, discussions have begun and both sides have laid out their initial points of view.
Trump’s legal team is seeking clarification on whether the president would be interviewed directly by Mueller, as well as the legal standard for when a president can be interviewed, the location of a possible interview, the topics and the duration. But the president’s team is also seeking potential compromises that could avoid an interview altogether, two of those interviewed told NBC News.
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In addition to the possibility of suggesting the president submit written responses in place of an interview, a second person familiar with the president’s legal strategy said another possibility being contemplated was an affidavit signed by the president affirming he was innocent of any wrongdoing and denying any collusion. It was not clear what such an affidavit might state regarding the president’s firing of former FBI Director James Comey in May 2017 at a time when Comey was leading the Russia probe.
Justice Department veterans cast doubt on the possibility that Mueller, who served as FBI director for 12 years, would forgo the chance to interview the president directly.
Senator Richard Blumenthal (D-CT), a member of the Senate Judiciary Committee, reacted to the news on Monday morning.
“Unquestionably there has to be that kind of face-to-face interview. The timing is important because the special counsel needs to have as many facts and as much evidence before he has that face-to-face interview with the president of the United States,” Blumenthal said on CNN’s “New Day.”
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“I think that the evidence accumulating against individuals within the White House, within the administration, the mounting evidence of obstruction of justice that’s public, and we have no idea all of what is available to the special counsel,” Blumenthal said when asked why he believes there will be more indictments.
Read More: Initial talks underway about Trump interview in Mueller Russia probe (NBC News)
Trump legal team has discussed possible presidential interview with Mueller's team (CBS News)
Blumenthal: Mueller has to have ‘face-to-face interview’ with Trump (The Hill)