International Automobile Federation (FIA) president Max Mosley will decide in June whether to stand for re-election, he said on Tuesday.
Mosley announced in April, after becoming embroiled in a sado-masochistic sex scandal that triggered calls for his resignation, that he would stand down when his term expires next October.
However the world motorsport chief, backed by success in a confidence vote, has since spoken of considerable pressure from members for him to stay in office.
The Briton told the official Formula One website (www.formula1.com) that he still had no plans to run for re-election but would make a decision in June.
"The difficulty is finding somebody who has the necessary experience, but also the time and inclination to do the job," he said.
Mosley, who has played a key role in forcing through cost-cutting measures in Formula One, said any candidate would need plenty of patience and "an ability to understand quickly a great variety of technical and legal issues.
"I would advise a potential successor to think very carefully before standing for election," he added.
On other matters, Mosley said Formula One still needed an independent engine supplier to protect against the risk of manufacturers pulling out due to the global financial crisis.
Honda withdrew this month, leaving BMW, Renault, Ferrari, Mercedes and Toyota to supply the nine remaining teams with engines.
"I think we ought to try to have at least one independent outside engine supplier, because of the risk that we will lose another manufacturer or even two," said the Briton.
Mosley was confident new rules for next season would produce more overtaking.
"The 2009 aerodynamic regulations were developed by three of the top Formula One engineers, aided by an extensive wind tunnel programme," he said.
"I have no means of judging whether they have got it right, but if they have not, it will be surprising and disappointing."
The new KERS system, harnessing energy generated by braking, could also make a significant difference to overtaking by giving each car an 80 horsepower boost for up to six seconds per lap.
The system is not mandatory however and some teams have already said they will not be using it when the season starts in Australia on March 29.
