F1 last had tyre competition in 2001-2006 after Michelin arrived to take on Bridgestone, the Japanese company having been on its own for two seasons following the departure of Goodyear.
From 2007, Bridgestone was the sole supplier for four seasons before Pirelli returned to the series in that role in 2011, after an absence of two decades.
FEATURE: Why tyre wars have largely become a thing of the past
F1 has stuck with a single supplier for cost reasons, and mainly because of the extra amount of testing that a tyre war would inevitably require.
There is also the belief that all teams running the same tyres level the playing field, and also does not allow teams contracted to a particular manufacturer to gain an advantage.
In theory, the conclusion of Pirelli's newly announced extended deal – at the end of 2027 or 2028 depending on whether an option for the latter season is taken up – could allow F1 to take a different approach, assuming that more than one company is interested.
However, Domenicali insisted that unless ways could be found to address cost, there will be no interest in having more than one supplier.
"I think that point was taken together with the FIA to make sure that we were able to control the costs of the ecosystem of F1," he said of the sole supplier arrangement.
"That was the main reason that we moved from the tyre competition, when we had a lot of testing, where we had a lot of mileage, and where there was a lot of research, that was really beneficial. But the cost was really massive.
"Therefore, that was the reason we moved from that direction into the new situation. It is too premature to consider that this could be a possibility for the future.
"In terms of an actual situation where the cost control is very relevant, I would say we haven't decided for sure, but it's not yet on the agenda to see if this could be a possibility in the future.
"But it's a point of relevancy, because in the future if you're able to control with different mechanisms, the cost, why not?
"But so far it's not on the agenda of the discussion together with the FIA, and with the teams."
Pirelli is expected to quit F1 at the end of its latest contract.
However, the company's executive vice president Marco Tronchetti Provera insisted that he welcomed on-track competition.
"I think that it is important to underline that Pirelli is participating as part of more than 300 championships around the world in the motorsport business," he said.
"In most of them, there are also other suppliers, and we are happy to compete with other suppliers. So it was never an issue for us.
"For us it has been always an opportunity, competing with others as we do providing tyres for the prestige cars, the premium cars. We are very happy because it's an opportunity to prove our technology."
