Heavily criticized for its 2013 tires, and now embroiled in 'testgate', the Italian supplier is also unhappy with F1's tight testing limits and the obstacles to tire specification tweaks being erected by the teams.
Facing the wrath of the FIA's new international tribunal for accepting Pirelli's invitation of a private test at Barcelona recently, Mercedes' team boss Ross Brawn on Friday sounded uncertain Pirelli will still be in F1 in 2014.
"Discussions about testing for next year will certainly be beneficial for whoever the tire supplier is in the future," he said.
Italy's La Repubblica said Paul Hembery repeated Pirelli's recent quit threat on Friday, "if we are unable to do some tests with the new tires before the start of the season".
"We cannot continue to work in the dark," he added. "By September first we need to provide the specifications for next year, but we don't even know what the cars are going to be like.
"We believe that the (2014) tire should be wider, but we don't know by how much.
"This year, because of the lack of tests … we ended up with these cases of delamination, and then because we couldn't go onto a track we had to remedy it in the laboratory."
And, still, the teams refuse to agree to the new tires debuting at Silverstone late this month.
"We have heard that Lotus will not accept any changes," Hembery is quoted by Finland's MTV3.
"If that's right, we will use the same tires for the rest of the season. There may be some more four-stop races, but what can we do?"
Indeed, Hembery said Pirelli may have to revert to using glue during the construction of the unchanged 2013 tires to stop the tread separating from the carcass.
"Either we get the agreement of all the teams, which I think is unlikely," he said, "or we will have to have some other ideas."
He is quoted by Italy's La Repubblica: "We don't want to have another season like this one.
"Our (F1) contract is expiring. Will formula one be without tires? I don't know, but that's not our business.
"Who knows, maybe they'll find another supplier willing to work in the dark."
Even Pirelli president Marco Tronchetti Provera is being asked about the 'tire-gate' scandal, telling Tuttosport: "It doesn't concern us.
"We have followed the rules and we will continue to do so."
Hembery, on the other hand, sees the situation as the moment to set out Pirelli's conditions for staying beyond 2013.
"We will wait for the tribunal, but then there will be several elements that need to be discussed. We are talking about issues that have a clear impact on our business.
"This is not just a matter of waiting for the truth to come out," he is quoted by Canada's La Presse, "but also a question of doing things differently in the future."
Germany's Auto Motor und Sport, meanwhile, took the opportunity to float a conspiracy theory.
"Does Jean Todt have a secret agenda, and wants Pirelli to get so angry that they leave voluntarily, opening the door to Michelin?" correspondent Michael Schmidt wonders. F1Pluss
06/05/13 Bridgestone has also ruled out a return to Formula 1 next year amid uncertainty over Pirelli's future in the sport.
The Japanese manufacturer, which came into F1 in 1997, pulled out of the sport at the end of the 2010 season.
A spokesperson has confirmed that there are no plans to reverse that decision.
"We have no current plans to re-enter F1," a Bridgestone spokesperson told AUTOSPORT.
"Since our participation in F1, Bridgestone has achieved a significant improvement in brand awareness in Europe and in other areas all over the world.
"At the same time, Bridgestone was successful in applying the technologies for compounds, design, and simulation for F1 tires for the development of passenger car tires.
"We can say that the participation of Bridgestone in F1 for 14 years was very significant.
"Under the current business environment which is continuously changing, Bridgestone focused on the need to redirect its resources towards the further intensive development of those innovative technologies and strategic products, and decided not to re-enter into a new tire supply contract after the expiration of the contract at the end of the 2010 season."
06/03/13 (GMM) Hankook has been in talks with Bernie Ecclestone about replacing Pirelli as F1's official tire supplier.
In April, we reported rumors that the South Korean company was an alternative to Pirelli, who are pushing hard for a new contract but also not ruling out quitting the sport.
But, over the weekend, reports emerged that a Hankook spokesperson had said a F1 foray was now "impossible" for 2014.
However, the Spanish newspaper Diario As correspondent Manuel Franco has revealed that Hankook representatives have in fact met "several times" with F1 chief executive Ecclestone.
06/03/13 Hankook has ruled out becoming Formula 1 tire supplier in 2014 if Pirelli does not agree a new contract. The South Korean company, which currently supplies tires in a number of categories including the DTM and the Formula 3 European Championship, is open to a move to grand prix racing in the future.
But the company's DTM competition engineer Michael Eckert has confirmed it is too late to consider such a move next year.
"For 2014, it's completely impossible not only because of the lack of tire development time," he told AUTOSPORT when asked about the viability of a move into F1 next season. "Even if Hankook wants to take three, four, five years to jump into Formula 1 as a supplier, the lack of testing opportunities would make it impossible. With the current cars and drivers, it's impossible [to test] so you need to find a suitable number of vehicles and drivers that would allow you to get some reliable feedback."
Eckert added that question marks over the long-term tire regulations would also make it difficult to commit to developing F1 rubber given the lead time required.
"Even if we started this year with the first tire test, it would take easily three years until you can finish a safe and performing F1 tire," he said.
"Now the regulations are changing; engine formula, chassis, and aerodynamics… nobody even knows about the dimensions of the tires for 2014 – they are still not fixed.
"It's not 100 per cent certain they'll continue with 13-inch tires. It might be 15 or even 17.
"It could happen in the next five years that F1 cars are on 18-inch tires."
Eckert confirmed that Hankook is keen to continue the expansion of its motorsport portfolio.
In recent years the DTM and European F3 have been added, as have Superstars, Auto GP and other high-profile series.
F1 will remain an option, although he stressed that no decision has been taken that it must end up there.
"It's not obligatory that F1 has to be the final destination series," he said.
"From an engineering point of view, F1 is the greatest challenge, but from a financial point of view it is a huge investment.
"You have to be ready with all aspects of your company, not only with the tire itself but the infrastructure regarding the logistics.
"Currently, all the Hankook tire production is in Korea and it would be a big help to have a European base like Pirelli does with Turkey.
"We are not ready to jump into Formula 1 for 2014, it's not our goal short-term.
"Certainly we will follow up on it and we are interested in new opportunities from a business point of view and also, from a branding point of view, to go into new markets." Yahoo Eurosport