But multiple authoritative Italian sources and insiders are now reporting from Monza that Montezemolo's annual visit to the Italian grand prix could be the scene of an official announcement.
Others, like the highly respected La Gazzetta dello Sport correspondent Pino Allievi, say Montezemolo could then make his post formally vacant at a Ferrari board meeting next Thursday.
The rumours - with some even suggesting Ross Brawn will become team boss while Marco Mattiacci steps up to the presidency - have even reached Ferrari's top driver Fernando Alonso.
"I don't know. I have only heard rumours," he told the Italian news agency Ansa.
"I have not heard anything from him (Montezemolo)," said Alonso. "He has always been the president since I was here.
"If it did happen one day that he is not there, then we will talk about it, but it would be something totally new."