The Dutchman will lead United against Leicester City today in his final game as caretaker manager.
Ruben Amorim takes charge on Monday and the Sunday Express says he and Van Nistelrooy will meet tomorrow to discuss the latter's role.
Van Nistelrooy has stated he wants to remain on staff with United, having originally been brought to the club over the summer by former manager Erik ten Hag.
But Amorim is bringing his former Sporting CP assistants Carlos Fernandes and Adelio Candido with him to United.
Van Nistelrooy said, "Yeah, let’s wait and see how that goes.
"I am calm, to be fair. I am trusting the process. I believe the outcome will be good because I believe that as long as I’m here, there is no news.
"I am here at Manchester United, so that is my focus. I am calm in that sense and whenever the communication takes place, I will see."