With F1's recent strict in-season testing ban having forced teams to rely on ever more complicated simulator technology, di Montezemolo thinks the time has come for a rethink.
He believes that the expense of simulators is now such that serious consideration should be given to a wholesale return to testing as it would be better for teams - and cheaper.
"It is a joke," said di Montezemolo during a lunch with media at Fiorano. "We have been forced to invest a huge amount of money in these terrible machines, artificial, instead of testing here [at Fiorano] and Mugello.
"If somebody has no money to do tests, it is better to race in GP2, in go karts or go and play basketball. I want to do testing to first of all give new drivers the possibility to drive cars and get experience.
"But I also want to give more opportunities to the public because from one race weekend to another it is silent in F1. There is nothing, nothing.
"Testing is also a good opportunity for the sponsors, to call the public. And tests are less expensive than building and developing every month the terrible simulator. This is something we have to discuss for the future."
Although di Montezemolo is aware that F1 costs are too high, he believes restricted testing dumbs F1 down - something he is vehemently against.
"I think in soccer if you want to compete in the Champions' League, you have to buy good players, you have to train sometimes even five times in a day. This is competition," he said.
"I think that it is ridiculous that in F1, from one side, we are not allowed to test, and from the other side we are forced to spend a huge amount of money in the windtunnel in which we develop aerodynamics that I cannot transfer any of to my [road] cars.
"I don't want it to seem that I am a conservative old fan of F1. I think if we were allowed to do more testing, the scandal of the tyres [in 2013] would not have happened because even for Pirelli it is very difficult as they cannot do too many tests."
F1's testing ban has been relaxed for 2014, allowing a number of in-season tests to take place following grands prix during the year.