Trump's lawyers have been involved in ongoing discussions with FBI investigators as part of the agency's probe into whether there was collusion between the Trump campaign and Russia during the 2016 presidential election, according to NBC.
Citing "a source close to the president," the Washington Post later reported that the special counsel's office could interview the president "possibly within the next several weeks."
The White House did not immediately respond to a request for comment.
The president's team is deliberating ways to avoid a sit-down interview between Trump and Mueller's team, sources familiar with the matter told NBC.
Some of the options being considered include submitting written responses to questions instead of a sit-down interview or filing an affidavit signed by the president asserting his innocence, according to the report.
Discussions about the alternatives began shortly after former campaign manager Paul Manafort was indicted by the FBI in late October for charges that include money laundering.
Trump's legal team met with investigators in mid-December, the first correspondence between the two sides since the special counsel completed interviews with White House staff, CNN reported at the time.
Trump has consistently called the investigation a politically motivated "hoax" and has been reluctant to acknowledge multiple U.S. intelligence agencies' conclusions that Russia sought to influence the 2016 election in Trump's favor.