House Oversight Chairman Jason Chaffetz said the Trump administration's pick of Robert Mueller as special prosecutor for the investigation into Russia is "as good as it gets" in terms of finding an independent overseer.

"His credentials are impeccable. He served in the Bush administration, the Obama administration. He is unassailable in terms of his credentials, his background," Chaffetz told Fox News host Tucker Carlson on Wednesday evening. "In the latter part of his career, he had nothing to prove. He has been silent politically. It doesn't get any better than Robert Mueller."

The Utah Republican said he was caught by surprise with the Mueller announcement and was not given any heads up about it by anyone in the Trump administration.

Chaffetz also decried the need for a special prosecutor in the first place. Former FBI Director James Comey had been overseeing the probe, but was fired by Trump last Tuesday.

"Look, I have not seen any evidence of actual collusion. Where is the actual crime that they think they need a special prosecutor to prosecute? I just — I haven't seen it. There has been a lot of flailing but that flailing started before January 20," Chaffetz said.

Chaffetz and Carlson joked that neither knew what the House and Senate intelligence committees, as well as the FBI's investigation, was actually regarding.

"Is it about, number one, it appears to be about Russian influence on the election. And then, was there any collusion? But does that seep out, and at what point is that lead off?" Chaffetz said. "For instance, the oversight committee, we are interested in these so-called the Comey memos ... I physically don't know where these lanes are."

Chaffetz was out of Congress for an emergency foot surgery from the last week in April until recently.