Van Gaal, currently coaching the Dutch national team, is widely expected to be the manager United choose to replace David Moyes, who was sacked last month after less than a year in charge at Old Trafford.
Former United keeper Schmeichel, who played for the club from 1991 to 1999, says van Gaal has the right character and experience to take on one of the biggest jobs in world football.
But he advised the Dutchman to appoint someone with intimate knowledge of the culture, history and traditions of the club - with Giggs his ideal candidate.
Schmeichel told Sky Sports News: "As a person van Gaal fits most of the criteria that's needed. I think that what is needed right now by Manchester United, is clear direction. And with van Gaal, everywhere he has been, there has always been a clear direction.
"Some of the places he has been at, that has led to outright war. But I don't think that is going to happen here. We have a certain way that we want to be as Manchester United and a certain way of playing.
"And we (United and van Gaal) are not too far from each other. The combination could be very good. I think it's very important to have someone who is extremely experienced.
"He's managed at Barcelona, Bayern Munich and he's managing the Dutch national team.
"He has the right experience, and he's the right age, in his 60s. It's important to have someone who is looked at as a mature person, with conviction."
Giggs, who took over from Moyes as caretaker manager until the end of the season, has spent his whole career at Manchester United.
And Schmeichel says the Welshman is the perfect candidate to be van Gaal's "cultural assistant".
"I think that's hugely important - the foundation of this club is its history, its tradition," the Dane said. "There is a way of doing things. It's a lifestyle - it's not just a football club, there is so much more to it.
"Van Gaal is a very intelligent man, I'm sure he will pick that up very quickly. But I think it's important that he has that cultural assistant.
"Ryan Giggs has been mentioned as his assistant. I think that would be fantastic. You've got the young guy - a man who has been there all of his life, more than any other player in history.
"You've got the culture, the history, to feed right into the manager. He will come with his own ideas, but combine those two things - that's great.
"That's one of the reasons it's important to have someone next to him who understands what kind of club it is."