Formula 1 teams are not equipped for the championship to revive a tyre war and believe it would be worse for racing than having a single supplier.
F1 has had one tyre supplier since 2007, with Pirelli taking over the responsibility from Bridgestone from 2011.
Pirelli's F1 era has been dominated by a demand for, and subsequent of, high-degradation tyres but last year Italian company secured a new deal that will run to the end of 2023.
F1 is preparing a major overhaul for 2021, including a switch to 18-inch wheels, with the emphasis on reducing costs and improving the quality of racing.
Pirelli has stated it would be willing to consider competing against a rival if F1 went down that route, but teams believe it is not an appropriate option.
"In the current generation of Formula 1 then multiple tyre suppliers don't really fit with the model," said Red Bull's chief engineer Paul Monaghan.
"We don't go tyre testing every week and tyres per se are not a prime performance differentiator so at the moment our current working philosophy, if you like, is to have a single supplier.
"It would change everything that is on the table now and I believe plans for the future if we were to bring in multiple suppliers.
"I don't know if you would close the field up or spread it out in that circumstance.
"At the moment, we're not really equipped to go down that route."
F1 has relied on one tyre supplier more often than not over the last 30 years, through Goodyear (1992-'96), Bridgestone ('99-00, '07-'10) and Pirelli ('11-now).
Racing Point technical director Andrew Green is adamant that having a tyre war would be detrimental to the spectacle.
"I think multiple tyre suppliers goes against the whole ethos of trying to compress the grid and improve the show," he said.
"You are going to end up with the haves and have-nots with respect to tyres.
"Currently we all have the same tyre and we can all do the same job, up and down the grid.
"I think the team that does the best job with the tyres should be rewarded for that so I don't think that's the right way to go for the show, to be honest."
The six previous seasons of tyre competition - 2001 to 2006 - included two of the most dominant in F1 history, thanks to Ferrari's partnership with Bridgestone.
McLaren team boss Andreas Seidl warned: "We should not forget that even in the years of the biggest tyre war, sometimes we had a total dominance of one team throughout the entire season.
"So I'm not convinced that this is the solution.
"It's simply important now that between the teams, together with the FIA and FOM, that we take our time to really define clearly what is the target letter for the tyres for next year and for '21."