Mueller is trying to determine if Trump's campaign advisers colluded with the Russian government to influence the election.
The investigation also reportedly involves a probe into whether the President obstructed justice when he allegedly asked ex-FBI director James Comey to drop an inquiry into former National Security Adviser Michael Flynn.
Flynn pleaded guilty in December to lying to the FBI about his conversations with the Russian ambassador, becoming the first senior White House official to cut a cooperation deal in Muellers inquiry.
Now Trump's legal team is pushing for a written question and answer, multiple media reports said.
There was no comment from Muller's office.
The White House and Trump has been saying that he is ready to cooperate as he has nothing to hide.
"Mr Trump's lawyers are expected to try to set ground rules for any interview or provide answers to written questions. If Mr Trump were to refuse outright to cooperate, Mr Mueller could respond with a grand jury subpoena," The New York Times said.
"The White House does not comment on communications with the Office of the Special Counsel out of respect for the Office of the Special Counsel and its process. The White House is continuing its full cooperation with the Office of the Special Counsel in order to facilitate the earliest possible resolution," an attorney, who heads Trumps private legal team, said.
The possibility of Muller seeking to interview Trump, another media outlet said is an indication that the investigation is entering its final phase.
"This is moving faster than anyone really realises," a source told The Washington Post.
Trump is comfortable participating in an interview and believes it would put to rest the questions about whether his campaign coordinated with Russia in the 2016 election, the person added.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)