Motorsport director Paul Hembery did not hide his impatience when he told reporters at the Monaco Grand Prix that time was running out for the Italian company to design and test tyres suitable for radically different 2014 regulations.
"Apparently on Sept. 1 we are meant to tell them (the teams) everything that they need to know for the tyres for next season. We are now mid-May so you can imagine how ludicrous that is when we haven't even got contracts in place," he said.
"So maybe we won't be here anyway..."
Asked how much of a maybe that was, and how seriously Pirelli were considering walking away, the Briton added: "At a certain point somebody has got to make a decision.
"Things are getting, as far as we can see, extremely serious because the changes next year are so substantial that the sport has to make a rapid decision."
Formula One is switching to a new 1.6 litre V6 turbocharged engine with energy recovery systems next season and the tyres will also have to change to cope with the new unit's characteristics.
Hembery said the indications were that the power delivery and top speed would be very different, the aerodynamic loads would change and even the size of the tyres was to be decided.
Wider tyres could be necessary to create grip, due to reduced aero downforce, and there was the risk of having excessive wheelspin.
Hembery would give no deadlines for an agreement with the teams, which would be further delayed if the governing FIA were to decide to put the contract out for tender, but Pirelli had set an internal one.
"It's not a case of maybe putting a harder compound onto this year's tyres," he said. "The changes are so dramatic that we probably need to do a thorough re-engineering of the tyre and that takes time.
"So the longer this goes on, it makes our job impossible and there comes a point where probably you say 'Well, we don't have time to do the job any more."
Pirelli's return to Formula One as sole supplier, replacing Bridgestone on a three-year contract from the 2011 season, was announced on June 23, 2010 - which could be seen as an indication of a likely deadline for renewal.
If Pirelli were to pull out, any other supplier - should one be found - would struggle to provide tyres from scratch in the time available.
Asked whether there was therefore a danger of no Formula One next year, Hembery replied: "You'd have to ask the teams that. We've been trying to say that something needs to happen and quick."
Pirelli have been under fire for introducing new compounds this season designed to increase the number of pitstops and overtaking opportunities.
Critics, notably champions Red Bull, say the changes have gone too far with drivers unable to race any more on tyres that deteriorate rapidly and in extreme cases can be good for barely a handful of laps.
Pirelli have agreed to change some structural issues with the rear tyres from the Canadian Grand Prix to prevent dramatic situations where debris causes the tread to peel off while the tyre itself remains inflated.