Pirelli could withdrew from F1 at the end of this season if a new contract for 2014 in not agreed soon.
Motorsport boss Paul Hembery has long made his desire for a new deal known. But instead of one being put on the table, Pirelli have been left waiting.
And unless a contract is forthcoming in the near future, the Italian tyre manufacturer could call it quits on their time in Formula One.
"Apparently on September 1 we are meant to tell them (the teams) everything that they need to know for the tyres for next season," Hembery said.
"We are now mid-May so you can imagine how ludicrous that is when we haven't even got contracts in place.
"So maybe we won't be here anyway..."
Pressed as to how serious the threat of quitting is, he 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."
The Brit added that Pirelli would need to make changes to their tyres in light of next year's massive regulation overhaul, which includes a swap from 2.4-litre V8 engines to 1.6-litre turbocharged V6s.
"It's not a case of maybe putting a harder compound onto this year's tyres," he added.
"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."