Zirkzee looks up to the AC Milan director, who had a spell with United under former manager Jose Mourinho.
Zirkzee said: “I would love it if, in a few years’ time, people said that my game looks a bit like Zlatan Ibrahimovic. The start, with the winning goal against Fulham, was nice. Then we lost twice - and you know that at a big club like Manchester United the attention then comes full on.
“I believe it will be fine. I've always had that. I never doubted it would still work out with my career. As a player, you gradually discover what you need to do to get to the top level and what you must cut out.
“The defeat against Liverpool was shameful. But when I see the team training, I do think we are on the right track. I missed chances against Liverpool. Did I get into the right position? Yes, but what is the point when the ball does not end up in the net?
“I had really good talks with Erik ten Hag. It's unfortunate that the start was disappointing, but we know what we need to work on. Yes, it is about adjusting. Whether it is also tougher than Serie A? Yes, it could be. At Bologna, we had ball possession very often. In England, I feel the game undulates much more. It’s up and down and indeed different.”
On his move to Old Trafford, Zirkzee added: “It all happened quickly in the summer. I was at the Netherlands training camp in Wolfsburg for the Euros when United's interest came in. I haven’t even said goodbye to the club and people at Bologna yet. I hope I will get that opportunity, because I had a great time there in an important time of my career.
“We are working here (at United) on me having to at the point of the attack to score goals. Now it’s my dream to be the No 1 striker for club and country. You train, you do your best and then you find out whether you can keep up with the level.”