Pirelli boss Mario Isola says a potential tyre showdown in 2025 would be bad for the sport insisting the drivers should be the "heroes of the show".
The Italian tyre manufacturers' contract expires at the end of the 2024 season with F1 opening a tender to tyre-makers to become the exclusive partner from 2025, as well as the F2 and F3 championships.
Pirelli has been the sole provider of rubber since the 2011 season after taking over from Bridgestone.
Reports have suggested that Bridgestone are keen to return to F1 and have made an offer to be the supplier in two years' time.
Bridgestone went up against Goodyear in the late 90s while they also faced competition on-track from Michelin between 2001 and 2006.
Isola is worried that a similar showdown between manufacturers could be to the detriment of the sport as it would end up being too focused on tyres.
He told Sky Sports News: "It's difficult. If you look at all the motorsport championships in the world, having a sole supplier for tyres is now a common approach. You save money.
"The risk is when you are in competition, the race is decided by tyres and not by the cars or drivers. We want the drivers to be the heroes of the show, not the tyres.
"We are happy to be part of the show and give our contribution to the show but not to replace drivers. That's not right."