The new F1 name was unveiled on Monday when McLaren confirmed the end of its 23-year partnership with Philip Morris and the Marlboro cigarette brand and announced a five-year deal with the German tobacco company Reemtsma, which owns the West cigarette brand.
Reports yesterday said Hill had been offered a pounds 12m deal by Ron Dennis, McLaren's managing director. Dennis has said that David Coulthard would return next year, but left the door open about the other seat, saying only that "the best available driver" would take that spot. Mika Hakkinen is driving this season with Coulthard.
Hill is 13 points ahead of his nearest rival, his Williams-Renault team- mate, Jacques Villeneuve, with three races to go. The next grand prix is at Monza, in Italy, on 8 September.
Alain Prost, the four-time world champion, is believed to be behind the attempt to land Hill. Prost and Dennis are close friends and Prost won his last world title in 1993 when he was teamed with Hill at Williams- Renault.
There has been much speculation surrounding Hill's drive next season, as his contract with Williams expires this year, and he has been open about wanting a much richer deal if he wins the world title. He is also reported to be in talks with Jordan Peugeot and the new Stewart Ford team, as well as Williams and McLaren.
Under the Marlboro partnership, McLaren won nine drivers' world titles, seven constructors' titles and 96 F1 races, but has yet to win a grand prix this season. Philip Morris is reported to be getting out because of the high cost of the sport.