There were rumours last season that the reigning world champion would join Ferrari, if not this year, then the next.
When asked if the two could be at Ferrari together, Di Montezemolo replied: "No, I don't think so."
The Italian also said that he "did not want two roosters in a hen house."
Alonso's current contract at Ferrari runs out in 2016 and the team have always admitted it is difficult to have two A-list drivers on the rostrum.
Di Montezemolo did not completely rule the possibility out and referred to the potential partnership as a "dream team" in an interview last month.