Alonso's future became the subject of speculation during the summer when he was given a public dressing down by di Montezemolo over comments he had made.
It also emerged that the Spaniard's management team sounded out both Red Bull and Lotus about their future driver situation, while McLaren is eyeing taking Alonso back as soon as 2015.
But di Montezemolo says relations with Alonso are much improved now, and that he has no worries about him leaving before his current contract runs out at the end of 2016.
"This [the speculation about Alonso's future] is something good for the press, sometimes good for the public," said di Montezemolo.
"I am very pleased with Fernando. He has a contract with us until the end of 2016.
"My only concern is to give him a better car.
"I have a lot of problems but the number one driver is not a problem. We will talk in two years time."
Can Ferrari hold on to Alonso?
Di Montezemolo accepts that Alonso was frustrated about Ferrari's lack of progress this year, but has reiterated that now is the time for his lead driver to work even harder with the team to turn the situation around.
"I understand, I share, I told Fernando that he arrived second this year, thanks to his capability rather than thanks to the car," he said.
"On the other hand I want a driver that even in the difficult moments he gives outside and inside stays very, very close to the team.
"This is the effort that I asked of him in the middle of the season. But I am very happy to have him on the team."