The choice was presented by Bernie Ecclestone, Formula One's impresario and a man who has a handle on these things. Even Ecclestone has been unable to manoeuvre Hill, sacked by Williams-Renault, into a drive which would give him a chance of retaining the title.
That leaves as the Englishman's best option Jordan-Peugeot, who yesterday confirmed one of their seats for next season would go to Ralf Schumacher, the 21-year-old sibling of Michael. The irony of Hill partnering the new wunderkind from Kerpen would be a delightful twist to the sport's fiercest rivalry of recent seasons.
Ecclestone, relishing the irony, as well as the commercial potential, said: "Damon could win the championship and retire. He might have to if all he wants is the chance to defend it, because unfortunately it looks as though he's not going to get that chance.
"The only thing he could do at Jordan is help the team and young Schumacher. He would have to accept he might not be able to win a race, let alone the championship.
"But if it means sacrificing any chance of the championship, he would be giving something back to the sport. Williams have won a lot of things while he's been there and he has 20 wins to show he's the best after Michael Schumacher."
Ecclestone could not resist a mischievous slant to the younger Schumacher's move to Jordan. "Damon could be doing what his own brother didn't want to do for him. Michael could have got him in at Ferrari but didn't."
As Michael points out: "It would be unfair for Ralf to be with me at Ferrari at this stage of his career. It is his first season and he needs to learn. Maybe later we can be together."
Hill, believed to be earning $7m (pounds 4.5m) this year and to have asked Williams for $15m next season, would probably have to settle for a maximum of $3m at Jordan. Also in the bidding are Stewart-Ford.
McLaren-Mercedes and Ferrari have made it clear they have no job for him and Benetton-Renault have been quoted $18m to buy Jean Alesi out of his contract, a figure that unsurprisingly appears to be proving prohibitive.
Hill, beaten to the championship by the older Schumacher for the past two seasons, said: "I thought the world could bear only one Schumacher but now there are two. I didn't know he had a brother till earlier this year."
Brazil's Rubens Barrichello has been released by Jordan and Martin Brundle has been offered work as their reserve driver, adviser and ambassador next season.
Against the backdrop of this hectic market place, Hill is completing his preparations for the day that ought to mark his championship success. Unless Jacques Villeneuve, his team-mate, beats him by four points, the contest will be over.
Hill, second to Schumacher in practice yesterday, was unhappy with the performance of his car but then Villeneuve managed only fifth fastest time.
PORTUGUESE GRAND PRIX (Estoril): Practice times: 1 M Schumacher (Ger) Ferrari 1min 23.554sec; (av 117.409mph); 2 D Hill (GB) Williams-Renault 1:24.281; 3 U Katayama (Japan) Tyrrell-Yamaha 1:24.359; 4 E Irvine (GB) Ferrari 1:24.477; 5 J Villeneuve (Can) Williams-Renault 1:24.764; 6 J Alesi (Fr) Benetton-Renault 1:24.803; 7 G Berger (Aut) Benetton-Renault 1:24.832; 8 M Salo (Fin) Tyrrell 1:25.234; 9 M Hakkinen (Fin) McLaren- Mercedes 1:25.403; 10 H-H Frentzen (Ger) Sauber-Ford 1:25.567; 11 R Barrichello (Bra) Jordan-Peugeot 1:25.592; 12 M Brundle (GB) Jordan 1:25.705; 13 P Diniz (Bra) Ligier-Mugen-Honda 1:25.944; 14 D Coulthard (GB) McLaren 1:25.980; 15 R Rosset (Bra) Footwork-Hart 1:26.065; 16 J Verstappen (Neth) Footwork 1:26.288; 17 O Panis (Fr) Ligier 1:26:422; 18 P Lamy (Por) Minardi-Ford 1:26.515; 19 J Herbert (GB) Sauber 1:26.700; 20 G Lavaggi (It) Minardi 1:28.356.Reuse content