Bridgestone is still pushing hard to replace Pirelli as Formula 1's exclusive tyre supplier from 2025.
Many in the paddock expected the FIA to have already announced the results of the current tyre supplier tender process.
Some teams think it is already too late for Bridgestone to be prepared enough for 2025.
"I think the main thing is that technically, these tyres are very challenging to make. And if you haven't done F1 for a long time, like one of the suppliers hasn't, how do you go through a very extensive test program?" said Haas team boss Gunther Steiner.
However, the FIA is believed to have actually green-lit the technical capabilities of both Pirelli and Bridgestone, with talks having moved on to commercial matters.
"Pirelli is said to have the best chances," Auto Motor und Sport correspondent Michael Schmidt said ahead of the Italian GP at Monza.
"Apparently Bridgestone has improved its offer," he added. "But if Bridgestone were to secure the contract, they would have only a year to prepare.
"The teams would then have to make 2024-spec cars available in order to create conditions that are as realistic as possible for Bridgestone. It is questionable whether it can all be managed in such a short time."
Steiner said it is obvious that the big teams will help Bridgestone develop, "but the other teams will complain about getting a disadvantage".
"We need to wait until it's decided who is getting the tyre contract and then we'll see if we've got a problem or not," he added. "But I think it will not be easy if there is a new supplier."
Alpha Tauri boss Franz Tost, meanwhile, admitted that it is still possible Bridgestone will win the day.
"It's good that there are two suppliers who want to provide us with tyres because this brings us additional money and a good situation for FOM," he said.
"But from the technical side, I think it's quite late now for a new supplier. Fortunately, it's not my problem," said the retiring team boss.
