The former United midfielder, who is part of the coaching staff at Old Trafford, believes the club will bounce back under the Dutchman after they finished seventh in the table under David Moyes last season.
The 39-year-old said: "The new manager is in charge now, we are on an unbeaten run and now we are looking to make a good start to the season with the first five games we have got (Swansea, Sunderland, Burnley, QPR and Leicester).
"Everyone expects Manchester United to contend for the title.
"We finished as low as we have done last season, but when the season starts again, everyone will expect. I am a fan, and I will expect us to be challenging again."
Butt, a United player from 1992 to 2004, says there is a strong desire in the dressing room to improve on last season's poor showing.
"It (that desire) is immense," he added. "In days gone by it has sometimes been when Man United are at their strongest - when they have had setbacks.
"We were always told in no uncertain terms that you had to step up to the plate, otherwise you were not going to be at the club for very much longer.
"I'm sure the new man in charge will say the same thing to the players. Hopefully the players will react, and I'm sure they will."
Asked for his impressions so far of the new boss, Butt said: "Positive. He is obviously a very in-control man. He has an aura about him - when he walks in the building, you know who the boss is, and I think that is very important.
"We had that with Sir Alex (Ferguson) for all those years and I think we have that now with Van Gaal. He walks into the building and he commands your respect.
"All the players look up to him as the leader and that is how it should be. From afar, when I've looked at him it looks like he takes no messing about and if anyone doesn't toe the line, I'm sure they will be out of the team."
Butt was part of United's 'Class of 92 along with David, Beckham, Paul Scholes, Gary and Phil Neville who filled the Old Trafford trophy room under Ferguson, but he feels their success will never be repeated in the modern era.
He added: "We had a manager in charge and a club that believed in that, but it is harder now with the immediacy of it all. Everyone wants things instantly.
"Owners that come in don't necessarily know a lot about football - they just know a lot about business, unfortunately. But that's the way football is. People don't have the foresight to wait and see.
"We played together since we were 12, 13. To prepare lads to come through takes a lot of patience and a good owner to say to a manager 'we are going to give you time and stand by you'.
"Unfortunately, for whatever reason, it doesn't happen now."