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Trump's attorneys have advised him against the interview over concerns that he could be charged with lying to investigators in the probe into Russian election meddling, according to The Times.
Trump publicly said last month that he would be willing to sit down with Mueller, but hedged it by saying it would be up to his lawyers to decide whether or not he would take part in an interview.
"I'm looking forward to it, actually," Trump told reporters last month.
Trump has been privately telling others that he wants to do the interview, believing it would clear his name in the probe into Russian election interference.
If Trump declined to sit for an interview, Mueller could try to subpoena him for one - a move that could create a complicated legal battle.
Trump's personal lawyer, John Dowd, has been taking the lead on a possible Trump interview with Mueller, and is urging against, the Times reported.
However, White House lawyer Ty Cobb has broken with the rest of the legal team and is siding with Trump in favor of an interview with Mueller.
Cobb has pushed for the White House to be fully cooperative with the special counsel, and has said in the past that he expected the investigation to be completed by the end of 2017.
Mueller reportedly wants to question Trump about the firing of former FBI Director James Comey and Trump's interaction with former national security adviser Michael Flynn, who pleaded guilty to charges in Mueller's probe last year.
Comment: Trump assuming he could clear his name by having a sit-down with the Mueller team seems to be assuming the probe is after the truth rather than it being an attempt at bringing false accusations against the President. Trump is swimming with sharks.