The Dutchman was appointed earlier this month following the sacking of David Moyes in April - with the Scot having failed to live up to expectations after 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-place finish.
Schmeichel, who won five Premier League titles, three FA Cups and the 1998-99 UEFA Champions League with United, believes Van Gaal can ensure the return of attacking football at the club.
"We've got someone who has managed at the very top of European football (at) Barcelona and Bayern Munich and he's with Holland in the World Cup," he said.
"So we've definitely got somebody who is vastly experienced and has won before.
"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.
"He'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 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 number one, so we're always going to be looking at number one," 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."
