The same goes for Utah Gov. Gary Herbert, whom Huntsman tapped to be his lieutenant governor and then handed the top job when he left to become the U.S. ambassador to China.
"I'm on record," Herbert said during a visit to Washington earlier this year. "I supported Mitt Romney in the past, and I've encouraged him to run again."
Herbert, whose wife Jeanette donated $1,000 to Romney in 2008, noted that Huntsman hasn't even said he's running, a point quickly brought up by Lee and Chaffetz.
Huntsman has resigned his ambassadorship effective the end of this month and is expected to decide soon after whether he will launch a presidential bid. He is already slated to speak in New Hampshire, home of the nation's first primary election, in mid-May.
Lee, a freshman senator, served as Huntsman's general counsel for 18 months beginning in January 2005, but Lee says it's too early to say whether he's backing his former boss.
"He's a great man," Lee said. But "he's not in the race yet. He's still a sitting U.S. ambassador, and until such time as he gets in the race, there's no point in speculating on what I might do."
But Lee also said he's partial to Romney, whom Lee supported in 2008, and for now, he's straddling the line and seeing how the field of candidates shapes up.
"I think Mitt's a great candidate, and I have great affection for Jon Huntsman," Lee said.
Chaffetz, who ran Huntsman's 2004 gubernatorial campaign and served as his chief of staff, said he has already told Romney he would back him if he runs, though the Utah congressman said he's still planning to talk to Huntsman when he returns from Beijing.
"I had, early on, told Mitt Romney I'd be very supportive of him do what I could for him," Chaffetz said, noting he was surprised when Huntsman hinted that he, too, might run. Chaffetz spoke by phone with Huntsman in March, and Chaffetz vowed to postpone any endorsement until he had time to sit down face-to-face with the former Utah governor.
"Officially, I am keeping my powder dry at the moment," Chaffetz said.
The hesitation on endorsements may not come as a big surprise, given some recent polls that have indicated Romney would handily defeat Huntsman among Utah Republicans. Romney, who turned the scandal-tarred 2002 Winter Olympics in Salt Lake City into a successful venture, won the state's 2008 GOP presidential primary with 90 percent of the vote.
Huntsman, too, was a popular figure in Utah. In 2008, he took 78 percent of the statewide vote in his re-election as governor.
Matt Canham contributed to this story.