Trump's opponents allege that the Russian interference helped him win the polls. But he denies any collusion between the Trump campaign and the Russians.
Mueller, the former FBI director, has interviewed several members of the Trump campaign, Trump's family members, colleagues in the Cabinet and present and former White House officials.
He has been seeking the interview with Trump as part of his investigation.
"I'm looking forward to itI would love to do that and I'd like to do it as soon as possibleI would do it under oath," Trump told reporters during an impromptu press conference outside the room of his Chief of Staff John Kelly at the White House.
Trump hinted that the interview might take place in the next couple of weeks. But quickly added that this was "subject to my lawyers".
"I guess they're talking about two or three weeks. I have to say, subject to my lawyers and all of that, but I would love to do it," he said.
"No collusion. There is no collusion," he reiterated.
Trump's lawyers have been talking to the investigation team led by Mueller about an interview, and the form it might take, US media reports said.
Investigators are assessing if the Trump campaign colluded with Russia to influence the election in his favour - a claim denied by Trump and Russia.
Investigators will also determine if Trump obstructed the inquiry.
The US intelligence community has already concluded that Moscow tried to sway the presidential election in favour of Trump.
At the press conference, Trump also said his Democratic presidential rival Hillary Clinton did not give interview to the FBI under oath.
"I couldn't have cared less about Russians having to do with my campaign. The fact is - you people won't say this but I'll say it - I was a much better candidate than her," he said.
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