New PSG coach Carlo Ancelotti has reportedly placed the Brazilian striker at the top of his wishlist after taking over this week.
But Gattuso insists the 22-year-old will stick with the Rossoneri.
"If it is said that PSG have made an offer for Pato, then maybe there is some truth to it," he told Milan Channel. "But he is still very young and I think he will stay at Milan.
"He must stay with us, the club and the coach have said it, and I am confirming it.
"He is a player with a great goal average and if people expect him to do more, then it is because he can do it."
Milan are currently second behind Juventus in the Serie A table on goal difference.