Van Nistelrooy's final game as caretaker manager will be Sunday against Leicester City before Ruben Amorim arrives.
Asked if he'd like the fulltime job in the future, the Dutchman said: "Yeah, of course.
"I thought this through well when I made the decision to come to United as an assistant manager or assistant coach. I knew that coming to Manchester United was for me a special occasion, where I felt I wanted to be part of this journey with the club in also an assistant role.
"I had clear ambitions to manage. I made the decision to sign a two-year deal as an assistant and I'm still in that frame of mind to stay in that capacity."
Van Nistelrooy added, "I think we've done very well so far. The players have reacted very well in the games. The focus now is to build on that and show that on Sunday, with a big game ahead and a massive three points that are there to win.
"I don't know if it will be very emotional. I take it very pragmatically as well, although I am proud to be able to fulfil this. We'll see how I feel on Sunday."