The former United and Netherlands striker will take charge for the first time when Leicester City visit Old Trafford in the Carabao Cup last 16 on Wednesday.
He was placed in temporary charge after Erik ten Hag’s sacking on Monday, with United 14th in the Premier League.
United have made an approach for Sporting manager Ruben Amorim, although he said on Tuesday that he has not made a decision on his future.
Van Nistelrooy spent five years at United as a player from 2001 to 2006, winning the Premier League, FA Cup, EFL Cup and FA Community Shield. He returned last summer as Ten Hag’s assistant.
“When I returned in the summer as Erik’s assistant, it was because I believe that Manchester United can climb back to the levels that I knew here as a player,” Van Nistelrooy wrote in his programme notes before the Leicester game.
“I still have that belief, but it will take time and a lot of hard work.
“We’ve seen the squad’s potential at times this season, but clearly not often enough.”
Van Nistelrooy, who managed PSV Eindhoven for a year from 2022, said United “can be unstoppable” when “players, staff and supporters pull together”.
It is unclear whether he would remain at the club if Amorim is appointed.
Van Nistelrooy said: “Even on an interim basis, it is a great honour to manage the club I love for however long I am asked to do so.”