Pato, who is set to start on the bench in Sunday's league game at Atalanta, has been strongly linked with a move to Paris St Germain in the January transfer window.
"Pato has to stay," Gattuso said.
"The club and the coach have already said so.
"He is a player with a perfect goal average and we expect more from him because he is capable of giving more than the others."
Pato has struggled with injuries this season and has scored just once in eight league appearances for the Rossoneri so far.
AC Milan coach Massimiliano Allegri is expected to field the team's top scorer Zlatan Ibrahimovic alongside Robinho in Milan's attack on Sunday.
The Rossoneri go into the encounter in Bergamo riding an 11-match unbeaten run in the league.
Milan's 2-0 triumph at Cagliari in the last round allowed them to move to second in the standings, level on 34 points with Serie A leaders Juventus.
They will have to keep a close eye on Atalanta striker German Denis.
The Argentinian leads the goalscoring charts in Serie A with 12, one more than Ibrahimovic.
"It would be great if I do manage to score on Sunday," Denis said.
"But this game is Atalanta versus Milan and not Denis versus Ibrahimovic.
"The important thing is that my team wins."
Atalanta, who are unbeaten at home this season, go into the encounter at the Atleti Azzurri d'Italia stadium on the back of a 4-1 triumph over Cesena that lifted them to 11th place.
Milan will be without captain Massimo Ambrosini, who serves a one-match ban.