Massa, who has yet to finish on the podium in 2011, will reach the end of his current contract with the Italian team at the end of next season.
"We expect great things from him in 2012, and then we'll decide how to proceed. Let's say he'll have to prove himself," said Di Montezemolo.
Di Montezemolo gave his team a mark of six out of 10 for a disappointing year.
"I'd give a five, which I'll raise to six considering the effort and the victory at Silverstone exactly 60 years after Ferrari's first win in Formula 1," he explained.
"The season started badly, we didn't interpret the regulations well and we didn't take risks in the technology of our project."
Di Montezemolo is certain that the team will perform better next year.
Only one race - Massa's home Grand Prix at Interlagos in Brazil - remains this season and the 30-year-old driver trails team-mate Fernando Alonso by 137 points in the championship standings.
Massa joined Ferrari from Sauber for the start of the 2006 season and dramatically lost out to Lewis Hamilton by a single point in the 2008 title race.
However, he has struggled for form following a fractured skull sustained during qualifying at the Hungary Grand Prix in 2009.
His progress this season has been hampered by a series of clashes and a deteriorating relationship with rival Hamilton.
"Massa has been with us for quite a few years," added Di Montezemolo.
"Even if he didn't have such a great season or much luck, we can't question the ability of a driver who was winning the title three years ago, and who has always been fast and competitive."