Republican and Democratic senators so far have an open mind about the possibility of appointing Judge Merrick Garland, President Obama's doomed Supreme Court nominee, to lead the FBI after President Trump fired James Comey.

The possibility was first floated by Sen. Mike Lee, R-Utah, who suggested him for the post and argued that he would be a much-needed consensus choice to replace Comey, who had drawn the ire of many lawmakers on both sides of the aisle over the past year.

Senate Finance Committee Chairman Orrin Hatch, R-Utah, took it a step further, and told the Washington Examiner that he has recommended Garland to fill the position, although he admitted it could be an "uphill" climb.

Lee said the move could help build consensus among constantly feuding Republicans and Democrats.

"I think it would be good to have someone nominated for the FBI director who could get votes from both sides of the aisle and who also has a strong law enforcement background, who has extensive experience as a federal prosecutor, including a federal prosecutor handling some pretty high profile cases. I think he fits that bill," Lee told reporters at the Capitol on Thursday. "There are other people who would also. But he certainly does."

Senators who hadn't heard of the idea yet on Thursday didn't immediately reject it out of hand.

"I haven't even thought about it," said Sen. Tom Udall, D-N.M. "I think our caucus feels right now that we need somebody that has the faith of the public, real integrity, and the ability to jump right in and do the job ... It's a very difficult thing when you're in the middle of an investigation in to put a totally new person in, so I don't know. I want to look at all the candidates we have, but I think he meets a lot of criteria."

Sen. Richard Blumenthal, D-Conn., said that he would support Garland if he were nominated.

Republicans also seemed open to the idea. Sen. John Cornyn, R-Texas, the second-highest ranking Senate Republican, called the possibility an "interesting idea," but wasn't ready to say if it was a realistic option.

"That's a great question that I don't know the answer to," Cornyn said.

One reason Republicans could support him is that it would create an open seat on the crucial D.C. circuit court of appeals, which Trump would be able to fill. When a potential vacancy was mentioned to Cornyn, he told a reporter that "you're getting my attention." That sentiment was shared by Sen. Roy Blunt, R-Mo.

"Well, he's a perfectly fine man who'd be better at the FBI than he would being a judge," Blunt told reporters. "It would also create a vacancy in the important D.C. circuit, so maybe I like it better the more I think about it."

Some Democrats, however, are deeply skeptical of any move and of the idea that Garland would entertain the idea. Sen. Dick Durbin, D-Ill., the number two Democrat in the Senate, equated the possibility to being a "consolation prize" after what happened to his nomination last year.

"After the way the Senate treated Merrick Garland, I hope this isn't some kind of consolation prize," Durbin said. "I doubt he would even consider it ... I don't think he'd be interested in that."

Susan Ferrechio contributed to this report