The Dutchman has yet to start in the Premier League since joining from Ajax this summer.
But after getting a chance to impress in the 5-0 win over RB Leipzig on Wednesday, Hargreaves thinks van de Beek will make him hard to drop.
"I think he's a really good player," Hargreaves told BT Sport.
"Everybody tried to get Thomas Muller out of the team, but once he's in, you can't get him out in terms of goals, assists, he's very unselfish, he can press the ball, he works in a midfield three, he can play as an 8 or a 10.
"[Van de Beek] is one of those... once he's in the team, Ole is going to find it hard to get him out."