Trump then questioned why he would be interviewed, arguing again there had been "no collusion" between his campaign and Russia.
"When they have no collusion — and nobody's found any collusion at any level — it seems unlikely that you'd even have an interview," Trump said during a news conference at the White House with Norwegian Prime Minister Erna Solberg.
Trump's comments Wednesday marked a shift from what he said months ago.
In June, after James B. Comey told a congressional panel that Trump had privately asked for his loyalty, the president said he would be willing to testify under oath to dispute the fired FBI director's claims.
"One-hundred percent," Trump told reporters when asked whether e would give a sworn statement to Mueller.
Mueller's team told Trump's attorneys in December they are likely to request an interview with the president, The Washington Post has reported, as part of its investigation of Moscow's meddling in the election and of whether any Trump associates conspired with Russian agents.
The investigation is expected to last for much of 2018, according to people with knowledge of the probe.
The wide-ranging probe has led to a guilty plea from former national security adviser Michael Flynn for lying to the FBI about his contacts with Russian Ambassador Sergey Kislyak and the indictment of former campaign chairman Paul Manafort, who was charged with conspiracy to launder money, making false statements and other charges in connection with his work advising a Russia-friendly political party in Ukraine.
Mueller has interviewed a number of Trump's senior aides and associates in recent months, including White House adviser and Trump son-in-law Jared Kushner, former chief of staff Reince Priebus, communications director Hope Hicks and White House counsel Donald McGahn.
"For 11 months they've had this phony cloud over this administration, over our government," Trump said. ". . . It's a Democrat hoax."
In response to questions about meeting with Mueller's team, Trump criticized the FBI's handling of its 2016 interview with Hillary Clinton, who was then a presidential candidate under investigation for her use of a private email server when she was secretary of state.
"When you talk about interviews, Hillary Clinton had an interview where she wasn't sworn in, she wasn't given the oath, they didn't take notes, they didn't record and it was done on the Fourth of July weekend," Trump said. "That's, perhaps, ridiculous, and a lot of people looked upon that as being a very serious breach."
Philip Rucker contributed to this report.