Stefano Pioli "cannot imagine" Milan without Gianluigi Donnarumma and says the club are convinced veteran striker Zlatan Ibrahimovic should stay for another season.
Milan director Ricky Massara revealed last week that discussions are ongoing over new deals for both players.
Donnarumma made his debut as a 16-year-old in 2015-16 and is contracted to the Rossoneri until 2021, while the short-team deal signed by Ibrahimovic in January has expired.
And head coach Pioli, who signed a two-year extension of his own last month, is eager for both players to pen fresh terms.
"I cannot imagine a Milan without Donnarumma," he told La Repubblica. "He is 21 years old, he already has experience and has even been captain.
"He is already among the top three or four goalkeepers in the world and will become the best."
Pioli added: "Ibrahimovic makes everything easy. It is wrong to refer to age with him. He is 100 per cent a professional and makes every training session competitive.
"Paolo [Maldini], [Ivan] Gazidis, Massara and myself are all convinced he should continue with us.
"From the economic perspective, it is right that I stay out of things, but we are all aware of what he has given us."
Milan ended the 2019-20 campaign strongly by going 13 games without defeat in all competitions upon their return to action in June.
Pioli was rewarded with a new deal and insists he paid little notice to speculation that Ralf Rangnick had been lined up to replace him during the close-season.
"Gazidis and the Elliott fund kept their word," he said. "They told me I would be judged at the end of the season.
"It didn't make sense to waste energy on things I was unable to control. I've not seen how Rangnick's teams play. I only concentrated on my own work with my players and staff."