The sport's chief executive Bernie Ecclestone dismissed as "complete nonsense" the Ferrari president's latest threat of a team-led series breakaway.
But Montezemolo, who in 2009 led the revolt against departed FIA president Max Mosley's budget cap plans, told international reporters last week that F1 is unlikely to proceed unchanged when the current Concorde Agreement expires in 2012.
"We need to think about what to do," the Italian is quoted by Germany's Auto Motor und Sport. "It can not go on as it is now."
Referring to the possibility of a breakaway championship, Montezemolo said: "Do we need the name formula one? I believe we could go on with a different one.
"We could continue with (owners) CVC, but only with better financial conditions.
"Or the teams start their own company and we give Bernie the presidency and we think of new and modern methods for marketing. We would do it along the lines of the NBA."
Montezemolo said he sees Ecclestone as central to F1's new format because of his "passion" for "racing and not the stock market".
Montezemolo does not hide his criticism of the sport's current governing FIA. "It cannot be that we give up everything that made our sport for the sake of costs," he said.
"F1 is about extreme innovation and technology."
Specifically on the 1.6 liter four-cylinder engines to debut in 2013, he admitted: "I can't get used to it. It's not for a sport in which we once had 12 cylinder engines.
"Ferrari will not stand in the way, but we are saying very clearly that we are not happy about it."