Schumacher is said to be on the verge of joining Ferrari, while Hill's possibilities now include an IndyCar drive with Newman-Haas.
The offer from the American team that took Nigel Mansell from Williams- Renault and Formula One at the end of the 1992 season has flattered and apparently perplexed Hill. It is believed to be worth pounds 3m for next year, about three times his current salary.
The Englishman, however, places the world title above all other considerations and is reluctant to give up the chase. He is confident that if he cannot pull it off this year, he is capable of mounting another challenge next season.
Hill said after arriving for Sunday's Hungarian Grand Prix here: "I have had one or two interesting phone calls this past week, without being more specific.It's nice to be recognised. But my priority is Formula One. I've still got unfinished business here. This is the pinnacle and my ambition is to be world champion."
Carl Haas, who co-owns the American team with the film actor Paul Newman, lured Mansell across the Atlantic after the English driver won the Formula One crown and failed to agree a new deal with Williams. He became IndyCar champion in his first season but struggled in his second.
Haas believes Hill can emulate the feats of the more successful Mansell. He needs a replacement for the departing Paul Tracy, but also insists he needs a decision from Hill soon.
Haas said: "Damon prefers to stay in Formula One but was not disinterested in IndyCars. He is a great driver, very much underestimated."
That kind of appreciation, as well as the kind of money on offer, would comfort Hill, who has always had to fight for what he considers just recognition at Williams. Should a satisfactory deal with his present employers or any other team in Formula One not satisfy him, he might yet go back to Haas.
Hill, like the other drivers, is awaiting Schumacher's decision, though he maintains: "It does not all depend on Michael."
Schumacher is adamant he has not yet made up his mind but is expected to give his verdict by the end of next week and Italian sources are confident he will sign a contract with Ferrari worth $25 million (about pounds 16m) for next season.
The Maranello hierarchy are said to have met his many demands - thought to include the selection of engineers as well as a fortune.
If the German leaves Benetton-Renault, the English-based team will almost certainly take the Frenchman, Jean Alesi, from Ferrari. Rumour has it the other Benetton driver could be Brazil's Rubens Barrichello, now at Jordan-Peugeot.
Hill's current partner, David Coulthard, is reported to be close to an agreement with McLaren-Mercedes. Jacques Villeneuve, has already tested for Williams and Germany's Heinz-Harald Frentzen is also being linked with any vacancy at Didcot.
Hill, trailing Schumacher by 21 points, had mixed views on a new edict requiring drivers to allow through any opponent who manoeuvres part of his car beyond the rear of his own car. Hill, ruefully reflecting on Adelaide last season, and Silverstone last month, said: "It's a bit late for me. On that basis Michael should have had to get out of the way in those two races. It's pretty amazing."
He added: "I have to go for wins for the rest of the season. Even if Michael gets seconds, I would have to win six on the trot to get ahead of him."Reuse content