Milan "have to be a little more ambitious" and aim to win more than just the Serie A title, according to director and club legend Paolo Maldini.
The Rossoneri won the Scudetto last season for the first time since the 2010-11 campaign after beating Sassuolo 3-0 on the final day, wrestling the trophy back from city rivals Inter.
Milan's attempts to lift the Serie A trophy for a second straight season have seen them win 10 of their opening 15 matches.
Yet despite sitting second in the table, leaders Napoli are yet to lose a game and already hold an eight-point lead over Stefano Pioli's men.
Milan have fared well in Europe, though, making it into the Champions League knockout stages for the first time since the 2013-14 season.
Maldini, who won seven Serie A titles and five Champions League trophies with the Rossoneri as a player, feels they should be looking for continental success to add to their domestic triumph of last term.
Maldini told MilanTV: "The match played in Sassuolo [to clinch the title on the final day] ended a three-year period that started in 2019 with a very specific project, which did not envisage the victory of the Scudetto, but envisaged the return to be competitive.
"Of course, we're talking about Milan, and we can't be satisfied with having won a Scudetto, we have to be a little more ambitious.
"We can and must be protagonists in the four competitions that remain to us, because little by little, they will be very intense months."
The World Cup has seen several Milan players undertake a starring role for their national teams in Qatar. France duo Theo Hernandez and Olivier Giroud are set to play in Sunday's final against Argentina.
Hernandez scored in the semi-final victory over Morocco and Giroud has become Les Bleus' all-time leading marksman, while winger Rafael Leao also netted twice for Portugal.
"Rafa [Leao] did his part," Maldini added. "Two goals in a World Cup is no small thing. Unfortunately, he didn't play much, but I think it was still a good and high-level experience for him.
"Olivier and Theo have been stars since the beginning. I must say that we are proud to see them in the starting line-up having reached the final of a World Cup."
Milan return to competitive action on January 4, when they take on Salernitana in Serie A.