Trump confirmed that his lawyers are in discussion with Mueller, who is leading the investigation into collusion between the US president's election campaign and Russia in the 2016 election, and also into allegations that Trump tried to obstruct his probe.
"I would love to do it," Trump told reporters in the White House when asked about testifying.
"I would like to do it as soon as possible... subject to my lawyers and all of that."
"I would do it under oath, absolutely," he added.
Special Counsel Robert Mueller departs the Capitol after closed door meeting in Washington. Source: AAP
Asked when an interview could happen, Trump replied that he didn't know exactly.
"Yesterday, they were talking about two or three weeks," he said.
Special counsel Mueller is believed to be focusing on whether Trump illegally interfered with the Russia investigation, particularly when he fired FBI director James Comey last year.
His investigators have been edging steadily closer to the White House, interviewing Attorney General Jeff Sessions last week.
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But the form of an interview with the president needs to be negotiated -- whether it is face-to-face, or in writing, or a mix -- and Trump told reporters he would listen to his lawyers' advice on how to proceed.
Trump has repeatedly denied any wrongdoing and has said Mueller will come up empty-handed.
"There has been no collusion whatsoever. There is no obstruction whatsoever," he said Wednesday.
Asked if he thought Mueller would be fair, he replied:
"We are going to find out... I hope so."
Mueller, the former FBI director named in May 2017 to lead the Russia investigation, has already issued indictments for four people from the campaign.
He has secured guilty pleas from two, former national security advisor Michael Flynn, and former foreign policy advisor George Papadopoulos, both for making false statements.
Both are believed to have agreed to cooperate in the Mueller investigation.
