The Red Devils great turned Reading manager has high expectations for the club he represented in the Premier League 79 times.
United have spent big against this summer and will be looking to greatly improve on last season's sixth-place finish.
They're back in the Champions League thanks to their 2-0 Europa League final win over Ajax.
And despite the added pressure that will bring, Stam expects a good showing from Jose Mourinho's men.
Stam said: "A club like United, you always want to win the league. It’s always their aim.
"It has to be their aim, to win the league.
"Bringing certain players in with a certain quality, it’s always been like that at United as well.
"You’re always looking as a manager, Mourinho as well, how last season went and what quality do we need.
"You’re going to be looking for that as a club.
"You can see now, with the signings that they’ve done, brought some great players in; quality-wise very good, experience-wise very good as well.
"That makes it interesting as well because if you look at the other teams as well, they’re all bringing good players in because they all want to win the league or do well in the Champions League."
