The Rossoneri fans are fearing an exodus of players after Kaka's big-money move to Real Madrid earlier this week.
World Cup-winning Italy midfielder Gattuso has been linked with a move to Chelsea, where former Milan coach Carlo Ancelotti has taken the reins.
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But his agent, Andrea D'Amico, has played down such talk.
He said: 'I have never said that Gattuso will leave. There could be offers for him by clubs because who wouldn't want a player like Gattuso?
'Rino (Gattuso) was saddened to see Ancelotti leave because he has a special relationship with him.
'(But) his mission is at Milan and he wants to stay.'
Gattuso, who missed most of the season with a knee injury, is currently on international duty with Italy in South Africa, preparing for the Confederations Cup.
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