Pirelli says it would have to "think very heavily" about its future in Formula One if Red Bull follows through with its threat to quit.
Red Bull is reaching a "critical" stage of power unit negotiations with Ferrari for next season for both itself and junior team Toro Rosso. Both could be absent from the grid next year following a series of threats from Red Bull about walking away from the sport it dominated in the early 2010s after growing disillusioned with the current engine formula and severing its contract with Renault one year early.
Pirelli, the sole tyre supplier for Formula One, is currently bidding to extend its contract beyond 2016 alongside Michelin. But the company's motorsport director Paul Hembery says it would be forced to consider its options if Red Bull was no longer in F1.
"It would make us think very heavily, yes," Hembery said when asked about a Red Bull withdrawal. "To lose two high quality, well-funded, professional teams -- and I can't imagine there would be immediate replacements, even though we have Haas entering next year -- then you are going to be worried.
"I know people say teams come and go, but we are talking about a very serious investment made over a significant number of years by Red Bull, and from our point of view, it would weaken the sport dramatically. For us, they are two very important teams."
Red Bull pulling its teams out of the sport would leave Daniel Ricciardo, Daniil Kvyat, Max Verstappen and Carlos Sainz without a drive for 2016. Hembery says Red Bull should be lauded for the work it does to promote young drivers to Formula One and for how it increases interest in the sport.
"We admire what they've done for the sport in terms of driver development; they work at grassroots, bringing drivers through to Formula One, from Sebastian Vettel to the four talents they have this year.
"They're also a team that goes outside of the Formula 1 circus to promote the sport, they invest significant sums of money in going to new locations, taking F1 to the streets of cities that don't stage F1 to try and create interest. So from our point of view, as a sponsor, any risk of losing both those teams would be a significant disaster for Formula One."