Under new coach Max Allegri, Milan sit third just two points behind Serie A leaders Inter Milan.
Pulisic told CBS Sports: "It's our goal, definitely. I don't want to look at it from the negative side, as it will be if we don't win.
"We'll do our best, we'll be judged game by game. There have been seasons where I haven't won anything, but we've done so many beautiful things. But when you win that trophy, there's nothing like it, it means your hard work pays off."
On his future, the USA captain also said: "Right now, I see about ten years of my career ahead of me. I want to keep going as long as possible. And now I see (Luka) Modric in the locker room: this guy is 40 and is performing like a 10-year-old.
"I wonder how he does it. I hope to do as well as he does."