The 25-year-old died last Friday following devastating brain injuries sustained in a crash at the Japanese Grand Prix on October 5.
Bianchi never regained consciousness after he hit a recovery vehicle head-on at the rain-lashed race in Suzuka and became the first Formula One driver to die as a result of injuries at a grand prix weekend since three-time world champion Ayrton Senna was killed in San Marino in May 1994.
The Frenchman was driving for the Manor-Marussia but he had been guided by Ferrari, who had helped secure his F1 debut and planned to switch him to Sauber for this season, and Di Montezemolo said he would have eventually replaced Kimi Raikkonen at the Maranello outfit.
“Jules Bianchi was one of us,” Di Montezemolo said.
“He was a member of the Ferrari family and was the driver we had picked for the future — once the collaboration with Raikkonen was over.
“He was first class: Private, fast, polite, very attached to Ferrari and promising.”
Di Montezemolo, who left Ferrari at the end of last year, added: “A bitter fate has taken him away from us, leaving us with a huge void.
“We lost a great guy, and we will remember him with great affection.”
Bianchi’s funeral will be staged in his home city of Nice today with executives from his Manor-Marussia team, FIA president Jean Todt and his son Nicolas Todt, Bianchi’s manager in F1, expected to attend.
Vijay Mallya, team principal at Force India, has become the latest F1 figure to pay tribute to Bianchi, describing him as “a tremendous talent” as well as “a friend”.
Bianchi was a reserve driver for the Silverstone-based outfit during the 2012 season and participated in nine Friday free practice sessions at various race weekends that year.
“The thoughts of everyone at Sahara Force India are with the friends and family of Jules Bianchi at this terrible moment,” said a Force India statement released from Mallya on their Facebook page.