The Dutchman was appointed on Monday following the sacking of David Moyes in April - with the Scot having failed to live up to expectations after Sir Alex Ferguson's retirement.
Moyes was often accused of negative and slow-paced tactics during his ill-fated reign at Old Trafford as the club went from Premier League champions to a seventh-placed finish and Schmeichel expects better from the highly decorated new boss.
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"A year ago we were talking about another new manager at the club, we were all hopeful and looking forward. We're doing the same thing again this year. Hopefully 12 months ahead we will be a lot happier because it hasn't been a good season.
"[Van Gaal]'s been a manager of Ajax a couple of times, he's been right in the core of creating the Ajax way of football so he's a guy who likes to see and watch football being played beautifully and effectively and trying to score goals.
"I think we have to wait and see but I'm convinced, going by where he's been, the way he plays with the Dutch national team, that's he's going to play attacking football."
Having seen the club relinquish their league crown this season, Schmeichel feels that Van Gaal should be targeting a title challenge in his first season.
"This is Manchester United we're talking about and the spirit of Manchester United or the core thought of Manchester United is that we're No.1 so we're always going to be looking at No.1," the Dane added.
"But, having had a season where we finished seventh, if we can get back into the swing of things and get qualified for the Champions League, that's going to be satisfactory - but of course we'll be looking to win the Premier League again."