The common perception in the paddock is that Ecclestone, 83, is resisting the modern era of the internet, and so Montezemolo said the likes of Google and Apple should come along.
He also said representatives of "new media" and "social networks" could have some advice to give.
Oddly in F1, arch-rival Mercedes appears to entirely agree.
"I had quite a long row with Bernie in a meeting," the German marque's F1 chief Wolff is quoted by the Guardian newspaper at Silverstone.
"We have lost 30 per cent of TV audience in Italy and we have lost some of the audience in Germany, although interestingly the UK is growing.
"Sure the (social media) model does not work yet as you cannot monetise it, but it is just a matter of time," Wolff added.
Mercedes' championship leader Nico Rosberg also agrees.
"We are here to entertain the people," the German is quoted at Silverstone by Speed Week.
"Social networks are a young, exciting and emerging media and an excellent platform to show the fans fresh perspectives of the sport. So we should take it seriously," added Rosberg.