It will be interesting to see how Massimiliano Allegri will deal with Massimiliano Allegri. I said last season that Milan's biggest problem was in defense, in attack they were fine. The thing is that Massimiliano Allegri is an expert in defending, so if he can strengthen Milan's defense and keep Milan's attack strong then I would say Milan will have a good chance of fighting for the title.
Now I don't know how many Milan players will not leave the team and how many will be signed. Milan is lucky to have the first ones: Cremonese, Lecce, Bologna and Udinese. If they win these 4 games, and then manage to beat Napoli then they will be well on their way to fighting for the title.
Milan had a lot of problems both in attack and in defense, so Allegri definitely has things to work on. But I have no doubt that he will manage to improve the defense because he is very good at that. As for the attack, in general they also have a few very good forwards, but by the standards of top clubs these players are at a middle level. So I do not know how much he can strengthen Milan without bringing in new players.
Milan needs to buy one or two strikers in order to strengthen their attacking force. Raphael Leao is a good player but he needs a good finisher which he can always cross the ball to, after he has put his opponent on the run from the left wing. Allegri is an experience coach and I believe that he will fix the club. By next season, we shall see the best of Milan.