The midfielder, a Rossoneri talisman having joined the club in 1999, made the largely unprecedented comments in the light of the global economic crisis.
"I think it could be a shared initiative but I think it depends on personal choices," Ancelotti told a news conference ahead of Sunday's Serie A match with Napoli.
"It is an issue linked to the strong sense of belonging that a player feels for this club and Gattuso has this sense of belonging."
Gattuso, out with a long-term knee injury, said on Thursday: "In times like this I'm in favour of an eventual salary reduction. If the club asks for a reduction from me, I'm ready."
Milan, who have significantly reined in spending, were already grateful that David Beckham gave up a large chunk of wages earlier this month to help extend his loan deal from Los Angeles Galaxy until June.
"I don't know if Beckham will allow me to reveal it eventually...but it is incredible what he has done to stay at Milan," chief executive Adriano Galliani told reporters on Saturday.
"Nothing like that has happened to me in 23 years as a club director. It more than stunned me."
Galliani called for a salary cap earlier in the week and said that a "wind of crisis" was blowing through the English and Spanish top flights as well as in Serie A.
He predicted that the close-season transfer market would be badly affected.
"A weak, pale summer market awaits us, with player swaps but very little money movement," he said. "This is more than certain."
‘After Manchester City’s recent form, maybe they’re the underdogs against Manchester United!’ Former Red Devils defender on this weekend’s derby
‘Arteta, Alonso, Emery, me… none of us were physical players – we needed the understanding of the game. That probably helped us move into management’: Premier League boss reveals reasons for natural career progression
