With their new contract waiting to be ratified, Paul Hembery has revealed that Pirelli could adopt a mixed approach to races in the future.
Pirelli have run the guantlet in both paddock and public opinion since taking over from Bridgestone as F1's sole tyre supplier in 2011.
But despite the criticism for tyres that wear too fast and tyres that don't wear fast enough, the Italian tyre manufacturer is set to stay on for a further three seasons from 2017 to 2019.
During the time Pirelli are considering taking a varied approach so that F1 fans see a mix of races with high tyre degradation and others drivers can "push" hard.
"We are still being asked to do two or three stops, that is the idea," Hembery explained to Motorsport.com.
"They want us to try to come up with a degradation that is probably similar to what we have seen in the past.
"Maybe we can come up with a variety of situations, with some races we can do with tyres that you can push on with minimal degradation, which is what you would do in open competitive, and then something a bit more akin to what we saw in the early years.
"It is a strange situation because, if you talk to the fans, they all loved that initial racing, and the monumental increase in overtaking manoeuvres.
"And from a spectacle it was interesting, but for the drivers it was such a big change that it was something they found difficult to deal with.
"Now we are somewhere in the middle. We are not happy this season doing one-stop races, it is not in reality what we have been asked to do. It is something we recognise and it is something we need to change in the future."
He added: "Maybe we should try in 2017 to have some races in that approach. Let's see the proof out there on the track.
"So, some races where you have high degrading tyres, some races where you can push, and let's see what produces the best racing."