Motorsport UK head David Richards said on Thursday he had been asked to stand for president of the International Automobile Federation, Formula One's governing body, and had not ruled anything out.
Frenchman Jean Todt, who has been FIA president since 2009, is standing down and an election for his replacement will be held in December.
British barrister Graham Stoker, Todt's deputy for sport, has already announced his candidacy and list of running mates, as has former rally driver Mohammed ben Sulayem of Dubai.
"I was asked to throw my hat into the ring and I'd consider it very carefully," Richards told Reuters after seven times world champion Lewis Hamilton opened Motorsport UK's new headquarters in Bicester.
"At the moment, as far we are concerned at Motorsport UK, we're waiting to see.
"I wait to see how both the current candidates are prepared to acknowledge the things that we think are important and how they are going to respond to those issues."
Richards, who did not say who had asked him to stand, added there was no need for an immediate decision on the "most appropriate" candidate to support, or whether to join them.
"I wouldn't say I've ruled it out but I think if there's an appropriate candidate that we can support then we will," he added.
Asked whether that meant "Watch this space", Richards replied: "I've been around motorsport all my life, and I know you never say 'never' on anything."
Richards, 69, won the world rally championship as co-driver to Finland's Ari Vatanen in 1981 and was also Formula One team boss of Benetton and BAR.
His Prodrive engineering company ran Subaru's world championship winning rally team and also is currently involved in the all-electric off-road Extreme E series with a team owned by Hamilton.
During his visit, Hamilton was presented with the Hawthorn Memorial Trophy, awarded annually to the most successful British or Commonwealth driver competing in the Formula One World Championship.
The 36-year-old has now won it 11 times.
"One day you're going to have to have a trophy after your name," Richards told him.
"What are we going to give the Hamilton trophy for in the future? Start to think about it now, give yourself a few years. We won't do it until you retire."
Hamilton, the most successful driver in the history of the sport with a record 98 wins and 100 pole positions, recently signed a new two-year deal at Mercedes.