John Grant, chairman of the British Racing Drivers' Club that owns the track, said in a letter to members that he is "hopeful" a deal can be agreed.

But he warned that "as things stand, 2019 could be the last British GP at Silverstone - or indeed anywhere".

Silverstone's contract to host the race ends after next year's event.

The track did have a contract until 2027 but last year exercised a break clause that enabled it to exit the contract after the 2019 race because they said it was becoming unaffordable.

F1's new owners, Liberty Media, have said they want to keep the historic races which they consider to be vital for the health and future of the sport. The British Grand Prix is one of them, along with the Italian, German and Belgian Grands Prix.

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A new contract with Belgium until 2021 was announced last month, but Germany is out of contract at the end of this year.

Grant's letter, seen by BBC Sport, said that Silverstone and F1 agreed on a number of areas:

• They "both recognise that the British Grand Prix is one of the 'iconic' GPs and, as such, is important to the future of the F1 championship and the value of the F1 brand"
• Both recognise that Silverstone is the "only realistic location" for a British GP, "at least in the near term"
• They agree that the Silverstone 'fan experience' is being improved and will improve further over the next few years
• Both want a deal that works for each party

The letter adds that despite efforts to "muster support from the British government... we should not assume any financial support will be forthcoming from government sources".

Grant's remarks contradict views expressed this week by Red Bull team boss Christian Horner, who said F1 had "a desire to see a street race in London".

Horner added: "F1 is going through changing times, lessons are being learned and there is so much competition that the BRDC are starting to move with the times."

Grant said Silverstone's aim in the negotiations was "to reduce the presently unaffordable financial risk of one or two bad years, and for Silverstone to make a reasonable profit on the event in a good year".

On the possibility of reaching an agreement, he said: "This will require compromise from each of us but must still broadly meet the objectives we have set out.

"There is plenty of time to get this resolved, and it's more important for us to get to the right answer than an early answer. Although the expression may have been first used in a different context, 'No deal is better than a bad deal'."

F1 was not available for comment but BBC Sport understands talks are ongoing and bosses are hopeful an agreement can be reached with Silverstone.