Milan executives will initiate the talks over prolonging the current Gianluigi Donnarumma's contract.
Donnarumma's current deal expires in 2018 and many see it as a measure of the Italian club's new owners' ambitions whether they extend the 18-year-old's deal or not.
Speaking at a first news conference since the Rossoneri changed hands for the first time in 31 years, Fassone said that work will start immediately on convincing the goalkeeper to commit his future to them beyond the end of next season.
"It's our priority," Fassone said. "We've also spoken about it already with the president. We want to resolve this quickly and make Gigio a pillar for our future. There are some contracts and discussions which will definitely be our priority."