The 24-year-old striker moved to Old Trafford in a £75 million deal this summer and is set to come up against Kompany in the International Champions Cup in Houston.

The City captain knows all about his qualities and has backed Lukaku to have another great season, which should end with them teaming up at the 2018 World Cup in Russia.

But Kompany's goodwill only stretches so far, and he is looking forward to starting a big rivalry when they face each other in the first ever Manchester derby outside England on Wednesday.

"I want him to do well -- except for in a few games this season!" Kompany told ESPN. "As long as we're ahead of them, I'm happy for him to do really well.

"The one thing you get when you have Romelu is an incredible drive to improve and to score goals. It's something really unique that I've been able to observe over the years because he's been a player from Anderlecht, which is the same youth system where I come from and I've really followed his progress.

"The key thing with him is he believes he's the best player in the world. It doesn't matter whether he is or he isn't, that's the way he approaches every single training session, that's the way he approaches every game.

"If you think you are the best you can never really be satisfied with yourself and therefore you always keep working harder and harder and that's what he does. It's a special player to have but there will be a lot of competition this season."

Kompany missed City's entire preseason last year through injury and he also missed much of the first six months of the season.

But he played in City's last eight matches of the campaign and now says he want to reach the stage where people stop taking about his injury problems.

"First of all, I'm always confident no matter what the situation is, that's why I come back otherwise I wouldn't be playing any more for this club," he added.

"The other thing is that I did miss out on the preseason last year but I don't like to attach my entire season to the fact that I'm training now with the team for a month.

"It's important but in a way whenever you're injured, you're constantly in a preseason so that's been the case for too much time for me.

"My dream is to achieve the end of the season and nobody ask me questions about my injuries any more."

Kompany is likely to line up alongside new signing Kyle Walker in the game against United, following the full-back's £45m move from Tottenham Hotspur.

The 31-year-old said he has already been impressed by the quality of Walker in the short time that he's been at the club.

"Kyle brings a sense of youth, strength, pace and he's someone I've enjoyed even in training, watching him go forward and watching him defending, he's already adding a lot to our team," Kompnay said.

"The main thing is I believe he can reach the next level with us. I believe that he's surrounded by players that will make him want to improve and by a manager that will give a lot of time and it's a good ingredient for him."