FIA president Jean Todt met with Pirelli chairman Marco Tronchetti Provera and its motorsport director Paul Hembery at Monza on Sunday to discuss the ongoing situation.
And although the final contract between the FIA and Pirelli is still not complete, sources suggest that it is now a formality for the deal to be sorted.
Hembery told Autosport on Sunday that he was optimistic things were finally moving forward, following weeks of uncertainty about the FIA's position.
"We have been having an ongoing dialogue with the FIA," he said. "We had a meeting this morning with the FIA and things are progressing along the right road.
That is the only thing I can say.
"With all these things, there tends to be a lot of legal aspects. So I cannot put a timescale on it - as lawyers seem to take an ever increasing time to complete things. It is all about the details."
Pirelli already has a commercial agreement in place with Bernie Ecclestone, and this week received the last of the contracts from the teams regarding its future supply deals.
Todt told Autosport that if the teams and Ecclestone were happy to remain with Pirelli then the FIA would accept a fresh deal with the Italian tyre manufacturer.