Van Nistelrooy was placed in charge of the 20-time English champions on a caretaker basis when Erik ten Hag was sacked last week, and the club's former striker guided the team to a 5-2 success over Leicester City in the EFL Cup on Wednesday night.
The Dutchman will lead the team in their next three games against Chelsea, PAOK and Leicester before Ruben Amorim arrives from Sporting Lisbon, with the Portuguese set to take charge of the team on November 11.
Van Nistelrooy's future beyond the upcoming international break is unclear, as Amorim has confirmed that he will be bringing in own staff, but according to The Sun, the club's players are desperate for the 48-year-old to remain at Old Trafford.
The report claims that the Dutchman is widely respected among the first-team squad, and the players have urged club chiefs to keep hold of Van Nistelrooy once Amorim arrives at Old Trafford.
Man United players 'desperate for Van Nistelrooy to stay at Old Trafford'
Van Nistelrooy famously represented Man United as a player between 2001 and 2006, scoring 150 goals in 219 matches for the Red Devils, before returning to the club as an assistant manager to Ten Hag over the summer.
The Dutchman said during his press conference ahead of Sunday's clash with Chelsea that he is expecting to revert to his assistant manager role once Amorim arrives in Manchester.
"It's going to be a short job as an interim, that was communicated very clear and I was happy with that," said Van Nistelrooy before it was confirmed that Amorim would be joining from Sporting.
"I felt I was called upon to help the club forward in this situation. Obviously, it was difficult that Erik had to leave, I was very disappointed, obviously with very mixed feelings about that but you have to switch the mindset to win because 75,000 people are waiting and celebrating and millions are watching at home. That's what we tried to do, same for Sunday and then we'll see.
"I decided to come back here for a very important reason that I'm here. I came as an assistant to help the club forward and I'm still very motivated to do so in any capacity. As an assistant, and now as an interim manager, and after that I go back to my assistant contract that I have here for this season and next. I'm very motivated to stay here and help the club forward, that's my absolute goal."
Will Van Nistelrooy remain at Man United?
Amorim confirmed on Friday night that he would be bringing his staff with him to Old Trafford, telling reporters after Sporting's clash with Estrela Amadora: "I'm going to take my coaching staff with me. We've been together since Casa Pia. It was one of the conditions."
Coaches Carlos Fernandes, Adelio Candido and Jorge Vital likely to move to Man United, but at this stage, it is unclear whether Amorim will find a spot in his coaching set-up for Van Nistelrooy.
It is clear that the Dutchman has had a huge impact on the Man United players since his arrival over the summer, though, and if he is able to navigate the team to some good results in their next three matches, then it would be surprising to see him leave.