President-elect Barack Obama’s transition team reached out to Utah Gov. Jon Huntsman Jr. about a possible appointment, the Republican governor said Thursday.

But Huntsman cautioned that he hasn’t filled out any paperwork and doesn’t believe an appointment is likely.

Huntsman, a former U.S. ambassador who supported Sen. John McCain for president, said Obama’s transition team called him for “a feeling out conversation” about his desire to help at some point with the incoming Democratic administration but that he was not asked about any specific position.

Asked whether he was being vetted for the administration, Huntsman said he didn’t know.

“I don’t know the answer because I don’t know what is going on behind the scenes,” the governor said in an interview with The Tribune’s Washington bureau. “I don’t know if there are certain Republicans under consideration. I really would have no idea in knowing if we were under consideration.”

Obama said in an interview with 60 Minutes on Sunday that there would be Republicans in his Cabinet, though he deferred on how many he would appoint. And the president-elect is reportedly studying President Abraham Lincoln’s appointments to his Cabinet, which he stocked with some critics.

Paul Light, a professor of public service at New York University who has studied the transition and political appointment process, says adding a Republican or two, or even three, to Obama’s Cabinet is a “low-cost option politically” and that the president-elect gains when he brings in members of the opposing party.

As a Western GOP governor, Huntsman also would bring diversity, Light says.

“Two things: Western Republican,” Light says. The Obama transition team is “currently under some fire — I think to a certain extent unfairly so — for filling up their key positions with Washington insiders.… A Western Republican would be a nice thing to have in the Cabinet.”

Huntsman was touted as a possible appointee had McCain won the White House because of his credentials as a diplomat. The governor has served as U.S. ambassador to Singapore and also as a deputy U.S. trade ambassador. He also speaks Mandarin Chinese.

For his part, Huntsman said he’s not interested in moving to Washington or an administration spot.

“I think we’ve already made our feelings known about coming back here,” Huntsman said about Washington. “We’ve got the best job in the world for one more term.”

tburr@sltrib.com