Trump made the comments to a group of reporters who were meeting with chief of staff John Kelly at the White House.
"I am looking forward to it, actually," Trump said, when asked if he was going to talk to Mueller. "Here is the story: There has been no collusion whatsoever. There is no obstruction whatsoever. And I am looking forward to it."
Trump suggested that people could wrongly construe his attempts to "fight back" against the investigation as obstruction.
"Now they're saying, 'Oh, well, did he fight back?' " Trump said of Mueller's investigation. "You fight back, 'Oh, it's obstruction.' "
Trump, during his exchange with reporters on Wednesday, said his interview would be "subject to my lawyers" but that he would personally like to do it.
Trump later said he would do the interview under oath.
"I would do it under oath. I would do it," he said, later adding, "I would do it under oath, yeah."
Responding to Trump's comments later Wednesday, White House lawyer Ty Cobb said, "While Mr. Trump was speaking hurriedly before departing for Davos, he remains committed to continued complete cooperation with the OSC and is looking forward to speaking with Mr. Mueller."
Cobb added that the arrangements are still being worked out between Mueller's team and the President's personal lawyers.
The special counsel investigation led by Mueller, a former FBI director, has seized headlines this week as a flurry of developments became public. CNN confirmed on Tuesday that former FBI Director James Comey and Attorney General Jeff Sessions have both been questioned by the special counsel, and sources confirmed to CNN that Mueller indicated interest in interviewing Trump, although it is not clear when the interview would take place.
Mueller's indicated focus is on the ouster of Michael Flynn as national security adviser and the firing of Comey in May.
Flynn has pleaded guilty to lying to the FBI about his contacts with Sergey Kislyak, who was the Russian ambassador to the US at the time, and said he was cooperating with Mueller's investigation into potential coordination between Trump associates and Russia to influence the 2016 election. Comey has said publicly that Trump tried to press him to drop an investigation into Flynn.
Trump has denied Comey's claims, which the former FBI director documented in contemporaneous memos, and previously said he would be willing to testify under oath.
But earlier this month, Trump dodged when asked about submitting to an interview for Mueller.
During a January news conference with Norwegian Prime Minister Erna Solberg, Trump suggested that an interview may not be needed.
"I'll see what happens. But when they have no collusion -- and nobody has found any collusion at any level -- it seems unlikely that you would even have an interview," Trump said.
Trump said last year that he would "100%" be willing to meet with Mueller.
Two sources familiar with the matter told CNN on Tuesday that Mueller has indicated interest in questioning Trump. The President's attorneys would like Trump's answers to come in written form only, but recognize it could end up being more of a combination of written and in-person interviews, or even solely an interview, CNN has reported.
Any interview between Trump and Mueller would serve as a likely crescendo in a months-long drama that has dogged that Trump White House.
The President also slammed Hillary Clinton for not being under oath during her interview with the FBI in 2016 which focused on her use of a private email server during her time as secretary of state.
"She didn't do it under oath, but I would do it under oath and you know she didn't do it under oath," he said. "Oh, I would do it under oath."