Two in-season tests after the Spanish and British grands prix have already been scheduled, but the official tyre supplier also wants to hold extra sessions in order to prepare for sweeping rule changes for 2017.
For the forthcoming wet tyre test at Paul Ricard, however, it is believed both Ferrari and McLaren will only field test drivers.
But for the 2017 tyre tests, Pirelli chief Paul Hembery said he wants the top teams to put its number 1 drivers on duty.
“We are facing a big change and we want to have the best teams and drivers to try the new products,” he is quoted by Italy’s La Gazzetta dello Sport.
Hembery said he wants the testing to take place in June and July.
“Two or three top teams with their top drivers, that’s what we need,” he added. “They raise the level because they are world champions. We want to test the fastest cars in the most extreme conditions possible.”
Meanwhile, Hembery admitted that while Pirelli has agreed a deal with Bernie Ecclestone, an actual contract for 2017 and beyond is yet to be signed with the FIA.
“I do not anticipate any problems,” said the Briton. “We have already signed with Ecclestone and the rest will follow.”