Bernie Ecclestone may reduce the staging of the British Grand Prix to every other year.
Ecclestone hinted the 56-year-old race at Silverstone, the oldest in F1, could alternate with the French Grand Prix.
"The French are happy to do that. As for the British race, I don't know what they want," he told Bloomberg.
But Stuart Rolt, chairman of the British Racing Drivers' Club who own the venue, told BBC Sport: "The idea was proposed and we said 'no thanks'."
The current contract to hold the British Grand Prix expires in 2009.
Negotiations to extend that term have been ongoing between the BRDC and Ecclestone, but Rolt says the two parties are some way off from settling on an outcome.
"I'm not confident a new deal will be struck, but hopeful," he added.
"Mr Ecclestone does want a British Grand Prix but at the end of the day Formula One is a business for him."