The 23-year-old midfielder has attracted interest from a number of clubs in Europe following his impressive performances for the defending French champions in Ligue 1 this season.
"He'll be staying," ESPN quotes Nicollin as saying. "We can't lose both [Younes] Belhanda and Cabella at the same time. [Benjamin] Stambouli and Cabella are important players.
"We want to keep the backbone of our team. Some players won't be kept, one or two will leave and two or three will come in, though 80% of the team will be the same as this season. We want to keep our best elements."
Cabella has been at Montpellier his entire career.