Paul Hembery reckons by changing the size of the tyres and introducing proper testing Pirelli could lower F1's lap times by "four seconds."
The sport is currently looking into various ways to make F1 cars fast and plan to introduce various changes in 2017.
However, Hembery says Pirelli can achieve that goal for F1 and that it would a lot cheaper than redesigning the cars.
"If you want to increase performance, we can do that," he told Autosport. "Just by the tyre size change we will probably gain two seconds.
"If you then gave us a proper testing programme, probably by the tyres alone, and with a natural evolution of the current car, we can deliver four seconds, and [the teams] won't need to do much else.
"It would be cheaper for everybody, and cheaper if they helped us do that than for everybody to redesign all the cars.
"Now maybe I'm missing something as to what else has been asked, but if it's just performance, then we can do that.
"And probably then we can provide a variety of compounds, maybe some in the direction as some have suggested where you can do stints of 15 laps, push as hard as you want and then you'll hit a cliff and change."
The Pirelli motorsport director added that very few changes will need to be made to the cars to accommodate large tyres.
"As a minimum you could just say 'change the tyre sizes and stick with the current regulations'," he said. "It then becomes a modification of the suspension.
"At least three teams have said they could modify a current car to at least take the tyre sizes if they were given enough notice without going the full packet of changing all the aero."