The Northamptonshire circuit's executive director Stuart Pringle has raised issues with the costs involved in hosting the race weekend and is unsure whether Silverstone can continue after the current contract expires.
Pringle told the Guardian: "I sincerely hope it won't be the end of grand prix racing at Silverstone but we've made clear to the Formula One management we can't live with the present contract beyond 2019."
Triple world champion Lewis Hamilton's success has attracted record crowds at Silverstone in recent years.
But the demands of the hosting fee, which goes up by five per cent every year - from £12million in 2010, to £17m this year and £26m in 2026 - has placed a heavy burden on the circuit's owners.
New owners Liberty Media hope to put plans in place to attract more fans to the sport, but Pringle stressed this was not a current issue at Silverstone.
"We are pretty much a full house and we are charging pretty much a full price and we still can't make the sums add up," Pringle added.
"Liberty have got some great ideas and we support their plans for a better show and fan experience. But they will likely take years to produce a significant benefit to the circuits and we haven't got the luxury of time.
"We need to deal in certainties and not possibilities."
Earlier this year, former F1 world champion Damon Hill, who was president of the British Racing Drivers' Club (BRDC) in 2009 when it signed a 17-year deal to keep the race at Silverstone, called on the UK Government to back the event financially or risk losing one of the country's best "shop windows".
In January he told Press Association Sport: "This is a much-loved national event but, for whatever reason, it has always been very difficult to get additional funding from government.
"Maybe now is the time to look at the British Grand Prix in the context of what is happening elsewhere and realise that it is an extremely good shop window for waving our banner and pointing to our brilliance in this field.
"When you think about post-Brexit Britain, you must wonder if this is exactly the type of thing we need to invest in to show off what we can do."
