The Scuderia have not won the driver's crown since 2007, while Red Bull have dominated both championships over the past four years.
However, speaking at the launch of the constructor's new car for the forthcoming campaign, Di Montezemolo said that the Marinello-based outfit have the ingredients to return to the top of the sport.
He said: "I'm confident because we have a strong team [and] two very strong drivers.
"I very pleased to have Kimi [Raikkonen] back as he was the last driver to win the world championship with us, while Fernando [Alonso] has had some fantastic seasons, finishing second in the past four years. Now it is time to win."
The season begins at the Australian Grand Prix on March 16.