The sport's existing tire supplier, Pirelli, has said a 2014 tender at this late stage would be "farcical".
But French marque Michelin, reportedly backed by the FIA's French president Jean Todt, said on Monday it is ready for talks so long as they begin soon.
The Michelin rumor gained strength at the weekend at Spa-Francorchamps, where Pirelli's fraught and highly-controversial season took yet another turn, when Friday practice was marred by more punctures.
"Our position is now known," Michelin's competition boss Pascal Couasnon on Monday told Le Figaro.
"If they (F1) are willing to talk, we are ready to do so.
"There must be a time when it is no longer possible — we still need the physical time to produce tires. By the end of October, it may be too late."
But he made clear that Michelin, who wants to supply 18-inch tires rather than the current 13-inch ones, is not simply willing to step into Pirelli's shoes.
Couasnon also said he is no fan of F1's new era of deliberately heavy degradation.
"How F1 is presented today I do not like it at all," he admitted. "It disappoints me and even makes me almost angry.
"F1 is not about changing a tire after a few laps, we offer a beautiful image of an important product for the automotive industry."