The Netherlands international has found it difficult to make his mark for the 20-time English champions this season, only managing one goal in 14 appearances, which came on the opening matchday of the 2024-25 campaign against Fulham.
Zirkzee has since gone 13 games without a goal, and there have been suggestions that he could return to Italian football as early as January, but Van Nistelrooy has backed the 23-year-old to come good for Man United.
"Josh is similar to Manuel Ugarte's situation. Josh came in, he's a young player with a lot of potential. He's a typical number nine in the sense of his hold-up play is very good, he's very strong in the combination play, he's a different type than Rasmus [Hojlund]," Van Nistelrooy told reporters when questioned on Zirkzee.
"Rasmus is more of a nine that plays higher up on the pitch, getting in the back of defenders and Josh is more the one coming to the ball and getting the team playing. The Crystal Palace game, he was excellent, it was one of his best performances and showed his potential.
"Another one with a lot of talent. A good age, a lot of potential to develop, look after, give him time, he will get better and better and better, and I think also will be a very good player for this club."
Van Nistelrooy "convinced" by "great player" Ugarte
Van Nistelrooy also addressed Ugarte, with the interim head coach "convinced" that the Uruguay international "will be a great player" for the club.
"I'm convinced about Manuel that he will be a great player for United. I think yesterday (vs. Leicester) he had a very good performance, against Fenerbahce he had a good performance," added Van Nistelrooy.
"Getting players in an early conclusion, players that are here for two or three months, you should be careful with that I think. It's a great signing, very good player, professional, he has very specific qualities in midfield, gets in between players, can recover a lot of balls for us to get us in attacking positions. Also, on the ball, very decent so I think he will be a very good player for this club.
"The recruitment is not part of the assistant manager, but I can comment on working with Manuel on a daily basis. He's adjusting, he wants to adjust, he wants to be part of this club, do well and he's very motivated to do so.
"He's getting better every time, the performance yesterday was good and he can build on that. We are very thin in midfield, the coming games, we're going to definitely need him and I think he'll do well in the coming games."
Will Zirkzee, Ugarte start against Chelsea?
Zirkzee is expected to start on the bench against Chelsea, with Hojlund set to feature through the middle, while Alejandro Garnacho and Marcus Rashford are likely to operate in the wide positions for the 20-time English champions.
Ugarte, though, is likely to be in the XI against Chelsea alongside Casemiro in central midfield, as Christian Eriksen is a doubt with the injury problem that forced him to miss the 5-2 success over Leicester in the EFL Cup.