It is believed the governing FIA has some powers to protect some of the sport's most iconic venues, like Monza and also the likes of Monaco, Spa and Silverstone.
But F1 chief executive Ecclestone has been making waves in Italy by warning that his current commercial deal with Monza is "a disaster".
"I don't think we'll do another contract," he added. "After 2016, bye-bye."
Hardened F1 insiders have seen Ecclestone's hard-nosed negotiating tactics many times before, but he is under pressure from other potential grand prix hosts who are willing to pay more.
One of them could be Mugello. The circuit near Florence is owned by Ferrari, and Luca di Montezemolo has made no secret he would like it to be on the calendar.
Apparently close to Ferrari in recent times has been Giovanni Malago, the Italian olympic chief who played down rumours the Maranello team is moving to muscle Monza out of F1.
"I rule out that Mugello intends to speculate on the issue on Monza," he is quoted by Tuttosport.
"But if there were problems that cannot be solved, it must always be taken into account that there is an extraordinary facility at Mugello.
"All of Italian sport, however, is rooting for the problems of Monza to be resolved."
Indeed, any suggestion that Monza could be axed is always guaranteed to touch nerves in Italy.
"Lombardy has always done its part for the Monza grand prix," regional president Roberto Maroni is quoted by La Gazzetta dello Sport, "but we hope that even the prime minister Matteo Renzi does not abandon his responsibilities.
"Monza is synonymous with the grand prix of Italy, and the economic reasons cited by Ecclestone are not acceptable or reconcilable with the history and the international role of Monza," he added.
For its part, Monza insists it is yet to speak directly on the issue of new contract terms with Ecclestone, Sport Business International reports.
Circuit chief Federico Bendinelli revealed that upgrades costing "at least EUR 10 million" will commence this year and "go on for the next four to five years".
As for Ecclestone's threat, however, the 83-year-old Briton "has not told us anything about this yet", he insisted.
"So we don't know what the new requests are for the Italian grand prix from an economical and commercial point of view," Bendinelli said.