Van de Beek has struggled for opportunities since joining Ole Gunnar Solskjaer's side from Ajax for £35m in the transfer window, but was named in the starting line-up for United's 5-0 Champions League victory.
The Dutch midfielder showed glimpses of his quality, combining play neatly and driving forwards with the ball at his feet, and Hargreaves insists Solskjaer will now find it difficult to drop Van de Beek.
"I think he's a really good player," Hargreaves said on BT Sport. "He hasn't had the opportunity to show it.
"He could be like what Thomas Muller is for Bayern Munich - the style. 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."
However, it remains hard to envisage how Solskjaer will incorporate both Van de Beek and Bruno Fernandes into his starting eleven, with the Portuguese midfielder making an immediate impact after being introduced from the bench in the second half.
Instead, Van de Beek may have to continue to wait for Solskajer to rotate his side. "Bruno and Marcus [Rashford] have played the last five, three for us and two internationals," the manager explained prior to the match.
"Scott [McTominay] played the last three plus three internationals. So five games in 14 days, six games in 17 for Scotty. You've got to look after the players.
"We have to cause them [Leipzig] more problems than they can cause us. I've picked a team we think can win the game and cause problems. I'll always pick a team I think can win the game."
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