Jackie Stewart insists it is unrealistic to expect the British Racing Drivers' Club to foot the entire bill for upgrading Silverstone.
The Northamptonshire track's future as host of the British Grand Prix is under threat after F1 chief Bernie Ecclestone's repeated criticism of Silverstone's facilities.
Ecclestone was also unimpressed by the incident in Sunday's race which saw a man run up the Hangar Straight.
Ecclestone has given the BRDC, owners of Silverstone, a month to commit themselves to a £40m upgrade of the circuit or risk losing their place on the F1 calendar.
But BRDC president Stewart believes that deadline is "unrealistic" as it does not allow adequate time to find partners to help with finance, which could include the government.
Stewart told BBC Radio 5 Live: "The BRDC, a private club, are being asked to raise this money.
"It is not possible, but we don't mind being among the players. Those players could include the British government.
"I do not think four weeks is realistic but the BRDC is keen to play a proportional part."
Stewart is due to meet Sports Minister Richard Caborn on Thursday.
"I've met Patricia Hewitt (Trade and Industry Secretary) and around 75 MPs.
"I'm meeting as many people as I can to make sure this is an all-party issue and to make sure they know Britain cannot afford to lose this industry."
Former world champion Stewart felt Sunday's race, which was won by Rubens Barrichello, was an outstanding spectacle and insists Silverstone served the crowd well.
"The crowd were comfortable. They used new roads that cost £17.1m. That was paid for by the BRDC, not the government."