Holland coach Van Gaal, who will take charge at United after this summer's World Cup, has already spoken of his desire to reclaim the Barclays Premier League crown for the club.
Hargreaves accepts a squad that finished seventh last season does need to be rebuilt but the ex-England international is convinced Van Gaal is up to the task.
Hargreaves, 33, whose four years at United from 2007-11 were ravaged by injury, told BT Sport: "If they can get the players necessary I don't doubt that Van Gaal could even lead them to the title
But they need to have a great summer.
"I doubt anything less than minimum Champions League (qualification) and even potentially competing for the title would be sufficient for him
I can't imagine him coming there to finish fourth.
"He has been so successful everywhere he's been, so I don't think they could have had a better option at this point.
"His sides play good football, they try and dominate possession and wait for that opening and I think United fans will be excited."
One of Van Gaal's first acts has been to appoint Ryan Giggs as his assistant manager, a move Hargreaves thinks could prove a shrewd one.
Hargreaves said: "Nobody knows Manchester United better than Ryan Giggs.
"He is arguably the greatest player ever to play for the club and still commands the respect of the current players and has that connection to the fans.
"To have Giggsy, with his knowledge of playing at Manchester United, learning under one of the most well-prepared coaches in the modern game - it's just a perfect combo."
Source : PA
Source: PA