Netherlands coach Van Gaal was confirmed as the new manager of the club on Monday, with Giggs becoming his assistant.
Hargreaves believes that the pair will lift the club following a disappointing season.
"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," he told BT Sport.
"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."
United finished seventh in the Premier League this season.