It was a season to forget for United in 2013-14, as they finished seventh in David Moyes' only campaign at Old Trafford.
Moyes was swiftly sacked in favour of the experienced Van Gaal, who has already overseen a change in formation, the Dutchman opting for a three-man defence, a system he adopted during the Netherlands' World Cup campaign in Brazil.
He also guided the club to an unbeaten tour of the United States, with wins against the Los Angeles Galaxy, Roma, Inter, Real Madrid and Liverpool in pre-season.
And Schmeichel claims Van Gaal's bold tactics - highlighted by his decision to swap goalkeepers in the Netherlands' penalty shoot-out win against Costa Rica - bode well for United.
"He did one or two things in the World Cup which were quite noticeable and have put his name right up there," Schmeichel told the Daily Mirror. "They were things no-one else ever dared to do.
"So he looks to be his own man, who knows exactly what he wants to do. I think we should be contending for the title again this season under him.
"He has always been someone who is at a big club like Bayern Munich and Barcelona and done good things. Hopefully he can do the same at Manchester United."
If United are to return to the top of the Premier League table, they must improve their home form.
United uncharacteristically lost 12 league games last season, with seven of those coming at Old Trafford, slipping up against West Brom, Everton, Newcastle United, Tottenham, Liverpool, Manchester City and Sunderland.
"It wasn't great losing that many games – especially at Old Trafford," the Dane added.
"If you turn those seven defeats into wins - which we would normally do - then you see we would have been right up there in the table.
"There was a problem at Old Trafford last season. It would be nice for that to go away and to see the team winning again - and hopefully in style."