The 48-year-old is currently in charge of the Red Devils on an interim basis, with Erik ten Hag losing his job on Monday, and he guided the team to a 5-2 success over Leicester City in the quarter-finals of the EFL Cup on Wednesday night.
Ruben Amorim is widely expected to become Man United's new head coach, but it is thought that the Sporting Lisbon manager will not officially arrive until November 10.
Van Nistelrooy is therefore set to lead the Red Devils in their next three games against Chelsea, PAOK and Leicester, but his future beyond that is unclear, as Amorim is set to bring in his own staff.
Speaking after the success over Leicester, Van Nistelrooy has said that he wants to "help the club further", although it is unclear at this stage whether there will be a role for him in the new coaching set-up.
Van Nistelrooy: "I'm helping as long as I'm needed"
"I came here as an assistant, to help the club, and now in this role, I'm helping as long as I'm needed. In the future, in any capacity, I am here to help the club further, to build towards the future," Van Nistelrooy told Sky Sports News.
"There are so many people around me who want the best for the club and that will never change. I think it's important to focus on Sunday, and the league game against Chelsea. What the future holds, let's wait on that."
Van Nistelrooy also thanked the fans for their support during his first game at the helm, while he praised the players for putting in an impressive performance in the EFL Cup contest.
"In the days leading up to this, it was with mixed feelings. Of course, I was sad to see Erik [ten Hag] go. He was the one that got me here. It was sad to see him leave but he's leaving the club with two trophies and can have his head held high. Of course, matchday comes and 75,000 fans are here and they support the team. They supported me in an unbelievable way," he added.
"As coaching staff, we prepared the players and I have to say they were fantastic today. Credit to the team, they pulled off a great performance today, after difficult moments. On the day it got announced, it was difficult for them and every one of us.
"Of course, when you have the manager is going, for us, as staff as well, so to react and play like this, it was a great achievement of the players. We promised to fight for the 75,000 fans and the millions at home watching and supporting United. For them, we wanted to show up, show this club is building and continuing to fight and never stop. That's what it is about."
Van Nistelrooy "delighted" for Fernandes
Van Nistelrooy also praised Bruno Fernandes for his two goals against Leicester, with the 30-year-old hitting the back of the net for the first time during the 2024-25 campaign.
"You know, with his qualities, we knew he just needed some luck to get the goals going and then they will come with many. I'm delighted for him. He's leading the team through many, many difficult phases and he's fantastic to have around," said the interim boss.
Van Nistelrooy's attention will now have switched to Sunday's Premier League clash against Chelsea, with the Dutchman almost certain to be in charge for the visit of Enzo Maresca's side.