Lukaku, who moved to Old Trafford from Everton during the summer, has scored six times in six appearances for United at the start of the 2017-18 campaign.
The Belgian international will look to continue his excellent start when Everton visit Manchester on Sunday afternoon, and Van Nistelrooy is "certain" that the 24-year-old will prove to be a goal-scoring machine for Jose Mourinho's side.
"Lukaku has made a good start at dealing with the pressure as a striker at United. There is always a price ticket around your neck, especially in the early matches. If you don't score, people say, 'Hey, he's not scoring'. But Romelu is scoring goals and I'm certain that will continue," Van Nistelrooy told reporters.
"Like me, I think he is a pure number nine, playing through the middle. You wouldn't put me on the wing. The same with him. I was the same type of player, making runs behind, dangerous in the box and holding the ball up.
"He has made a real difference to United. He has scored goals from the off and has the right boss, in Jose Mourinho, to guide him. There will be difficult phases to come. But Mourinho has been there and done it and will know how to guide him through any rough patches."
Van Nistelrooy scored 150 goals in 219 appearances between 2001 and 2006.