The President's legal team has been preparing for the expected request for months. Trump's lawyers have said they are hoping for the investigation to wrap up quickly.
However, the sources insisted there have been no substantive talks or active negotiations yet about a potential interview with the President. The matter was broached in a previous meeting and both sides are expected to explore it further in coming talks.
Trump's team would like to structure any agreement for the President to be interviewed by the special counsel. The President has expressed his eagerness to bring an end to the investigation as quickly as possible, according to one source with knowledge.
The expectation is that Mueller's team would not wrap up the investigation without an interview with the President, according to another source with knowledge.
Trump's team is looking to how previous administrations have handled requests like this in the past as a basis for limiting the President's exposure: whether he actually needs to testify under oath, whether he can provide written answers to questions from Mueller's team and whether the testimony should be recorded. Trump's attorneys don't want their client to be interviewed by the special counsel's team on a fishing expedition, according to one source with knowledge.
White House special counsel Ty Cobb stressed an overall willingness to cooperate with the Mueller investigation.
"For the record the White House does not comment on communications with the (Office of Special Counsel) out of respect for the OSC and its process. The White House is continuing its full cooperation with the OSC in order to facilitate the earliest possible resolution," Cobb said in a statement.
A spokesman for Mueller's team declined to comment.
It is unusual for a sitting president to speak directly to a special counsel or independent prosecutor who is leading an investigation. Previous presidents have sat down for a deposition in a civil suit.
One exception came with Ken Starr's investigation during the Clinton administration. In the summer of 1998, Starr's office subpoenaed President Bill Clinton to testify before the grand jury. After several days of negotiation between the President's lawyers and Starr's team, the independent counsel withdrew the subpoena. Clinton testified from the White House before the grand jury via closed-circuit television, which was taped and later publicly released. He also gave interviews under oath at the White House which were used as transcripts before the grand jury.
During the Iran-contra investigation in 1987, independent prosecutor Lawrence Walsh reportedly weighed whether to interview President Ronald Reagan in person or accept the President's written testimony. It was later decided that Reagan would submit written answers to Walsh's questions.
Over the weekend, Trump did not dismiss the idea of talking to Mueller's team. When asked by a reporter if he would meet with Mueller, Trump said, "yeah," and then said there has been no collusion and no crime, and did not clarify his answer about a potential meeting.
In June, Trump said he was "one hundred percent" willing to testify under oath about his interactions with former FBI Director James Comey, which could now be part of an obstruction of justice investigation.
Starr said Monday that it's "probable" that Trump will need to meet with Mueller before the special counsel can complete his investigation.
"(Mueller) needs to, in order to round out, complete his investigation, to come to a decision. He needs to look the President in the eye and ask the appropriate questions," Starr told CNN.
Democratic Sen. Richard Blumenthal echoed Starr.
"Unquestionably there has to be that kind of face-to-face interview," Blumenthal said, on CNN earlier Monday. "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."
How the President talks to prosecutors would be just as important. Starr said that a meeting would likely be negotiated between the lawyers. Because of the dignity of the presidency, it's less likely the special counsel would subpoena a sitting president.
For the most part, interviews in criminal investigations are voluntary. Trump couldn't be forced to speak directly to Mueller or the FBI; he could only be compelled to testify before a grand jury.
Trump's lawyers could be present for an interview with Mueller's team. Grand juries don't allow defense attorneys in the room during proceedings.
Trump is no stranger to testifying in civil suits. In January 2017, while he was President-elect, Trump gave an interview under oath as part of a lawsuit between his company and chef Jose Andres, who pulled out of a deal to open a restaurant in Trump's Washington hotel after Trump made disparaging campaign trail comments about immigrants. The lawsuit ended with a settlement, and the transcript is still confidential.
This story has been updated.