Van Gaal is expected to be unveiled as David Moyes' successor next week after United relinquished their league crown with a seventh-place finish this season.
The outgoing Netherlands head coach will be tasked with bringing UEFA Champions League football back to Old Trafford with a top-four finish.
However Schmeichel, who won the Premier League and Champions League amongst other titles during his eight-year spell at United, believes Van Gaal will be aiming higher.
"The club needs a strong man to steer us back up,' the 50-year-old told the Daily Express.
"We have finished seventh, so the top four is a good target to set yourself for next season.
"But Van Gaal will not want to accept the top four - he will try and win."
While Van Gaal is yet to be confirmed as United manager, it has not stopped talk of potential transfer targets, with the club expected to invest heavily during pre-season.
Germany internationals Toni Kroos (Bayern Munich) and Mats Hummels (Borussia Dortmund) have been linked to United, while Luke Shaw (Southampton) is tipped to join the club as they bid to return to the summit.
And Schmeichel has given the German pair his seal of approval, should they arrive in Manchester.
"United have got (Phil) Jones, (Chris) Smalling and (Jonny) Evans but going by what the media are saying, Hummels is a target," the Dane said.
"That's a good starting point to bring him in. He has good leadership skills and he is a fantastic defender. He's someone we've been looking at for a couple of years and he's been heavily connected with United."
