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 it I would love to do that and I'd like to do it as soon as possible I 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.
He was responding to a question whether he was ready for an interview with Muller who wants to question him about his decision to fire his former national security advisor Michael Flynn and FBI director James Comey.
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 said his presidential rival Hillary Clinton did not give an interview to 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.
"You will always say, she was a bad candidate. You will never say I was a good candidate. I was one of the greatest candidates.
Nobody else would have beaten the Clinton machine, as crooked as it was. But I was a great candidate, something you would not say that" he told reporters before he left for Davos.