The British driver had hoped to be world champion before determining his future, but defeat at the hands of his Williams-Renault team-mate, Jacques Villeneuve, in the Portuguese Grand Prix in Estoril has forced him to revise his strategy.
Although he remains clear favourite for the title, Hill is conscious one false move in the final race, in Japan in two weeks' time, could ruin everything. Without the No 1 to carry on a car, he would not present such an attractive proposition and must feel he cannot afford the risk of having offers withdrawn.
Interested parties have been asked to respond to what amounts to a questionnaire compiled by Hill and his representatives. They are required not only to state the financial terms for a two-year contract but also to provide information about working budgets, facilities, technical potential and team plans.
Hill, discarded by Williams and evidently shunned by the other "first division" teams, Ferrari, Benetton-Renault and McLaren-Mercedes, is resigned to relegation, with Jordan and Stewart known to be keen to sign him.
Both, however, suspect rivalry from Ligier, the French-based team owned by Flavio Briatore, who happens also to be the boss of Benetton. The prospect of being "in house" might entice Hill. He would be conveniently on hand should a vacancy suddenly appear at Benetton during next season or, at the latest, in 1998.
Jordan, the front-runners since a direct route to Benetton was blocked by Jean Alesi, fear they may not be able to match the retainers offered by the other teams. A ball park figure of $3m (pounds 2m) a year has been suggested.
Another factor Hill will doubtless consider is that his team-mate at Jordan would be Ralf Schumacher, the younger brother of Michael. The older Schumacher was hugely amused at the thought of partnering Hill at Ferrari. If Hill were now out-paced by Ralf, it would be too embarrassing to bear.
But then Hill must confront that sort of possibility wherever he goes, even at Stewart, portrayed by some as a safe haven because, as a new team, they will be given time to develop. Hill maintains he is undaunted in any company and, until Sunday, appeared to have the measure of Villeneuve.
This race left us with a different perspective and Hill's demise met with scant sympathy from his bosses at Williams, who must feel his lack of pace vindicates their decision to unload him. By Hill's admission, he was simply not quick enough.
Fortunately for him, he requires no more than a point at Suzuka, and that only if Villeneuve wins. All Hill asks is to be given a trouble- free run. Patrick Head, Williams' technical director, acknowledges the pressure is on the team to provide both drivers with reliable equipment.
Hill could, of course, conclude proceedings to his own advantage by driving Villeneuve off the road. It would, after all, not be the first time the championship has been decided in such a summary manner. But Head said: "I can't imagine Damon doing that. I would never question his sportsmanship. It wouldn't happen. It's not the style of the man. I expect Damon to win it fair and square."Reuse content