Ronald Reagan made it all the way to White House, Clint Eastwood managed a term as mayor of Carmel-by-Sea and Arnold Schwarzenegger is still, just about, governor of California. Now Val Kilmer could be the next ‘big-name’ to jollify the colourful world of celebrity politics.

The occasionally outspoken actor has sent a shock wave through the sleepy political establishment of his native New Mexico with reports that he is considering a run for the governor's job when the position becomes vacant in 2010.

Speculation about the bid was fuelled by Bill Richardson, the state's current governor, who told television reporters last week that he thought Governor Val Kilmer would be "a fine idea".

"I like the idea," he told a press conference. "Val Kilmer is a first-rate New Mexican. He was Batman. You know, there have been successful actors going into politics. I haven't talked to him about it, I don't know how serious he is, but you know if he jumps in a race he's got name ID, so it can't be discounted."

In the five days since those comments were made, Kilmer's spokesman, David Unger, has declined repeated requests to confirm or deny his client's political ambitions, only adding to the air of fevered excitement in the state's legislative capital, Santa Fe.

Reporters also unearthed comments this week that the 48-year-old actor made in January, when he appeared to float the idea of a political career. "I did get some lobbyists once saying that I'd make a good governor," Kilmer said. "Reagan wasn't much of an actor and look how that worked out for him. And then there's Arnold ... I think you should be able to pronounce the name of the state."

They note that Mr Richardson, a prominent Democrat who until recently was a leading contender for his party's vice-presidential ticket, is known to be friendly with Kilmer, and say that he is unlikely to have spoken without at least some inside knowledge. The actor, who apart from Batman Forever is best known for his roles in Top Gun, The Doors and True Romance, certainly boasts a decent enough pedigree for the job. He has lived in the mostly rural desert state since the early 1980s, and owns a 6,000-acre ranch near Rowe, about 20 miles south-east of Santa Fe, where he has a herd of bison. Quite what political ticket Kilmer might stand on is anyone's guess, though. At present, he's neither a member, nor a registered voter, for either political party, and state records reveal that he has never taken part in an election there. Although he recently cancelled an appearance at the Democratic convention in Denver, that should not be taken as a party endorsement: he was due to be speaking alongside the independent presidential candidate Ralph Nader.

Experts believe that Kilmer's left-leaning sympathies, together with his maverick streak, indicate that he would stand for office as an independent. However, no independent has ever won the governorship of New Mexico. In addition, a controversy from the actor's past may return to haunt him during an election campaign. In 2003, Rolling Stone magazine quoted him saying he "lived in the homicidal capital of the south-west", and that "80 per cent of people in my county (San Miguel) are drunk". Although Kilmer claimed his words had been taken "out of context", he was later forced to apologise.

Any future bid would also set Kilmer against the political establishment. Mr Richardson's current deputy, Diane Denish, has until now been strongly fancied to succeed him when his term runs out in 2010. This week, she seemed rattled by queries about whether Mr Richardson was now endorsing Kilmer. "There's a lot of speculation about 2010. But what I'm doing, and what I think everyone should be doing, is working on 2008," she said. "I'm not going to speculate on what the governor thinks." If Kilmer is to seek office, he will soon also have to start raising funds — a task that could prove problematic. Given Schwarzenegger's troubled reign in the nearby state of California, New Mexico's political bankrollers could be wary of another celebrity governor. Despite being comfortably off, Kilmer is unlikely to boast the sort of wealth necessary to finance a bid. His career has been in the doldrums of late, and his most notable recent role was as the voice of Kitt, the car in the new Knight Rider series.

But whatever happens, America's headline writers will be hoping a bid does materialise — it would afford them the opportunity to tip their hat to the role that made him famous in Top Gun and announce that ‘the Iceman cometh".