The temporary manager was fired by his replacement Ruben Amorim when he planned to return to his assistant position.
The previous Manchester United striker resurfaced to Old Trafford in the height of summer to work with Erik ten Hag and was named interim manager after his compatriot was fired on October 28.
Van Nistelrooy was eager to continue in his job following Sunday's 3-0 Premier League victory over Leicester, which capped an unbroken four-match run in command.
However, that was his final game with United, as Amorim chose to allow him depart in his first choice as manager.
Amorim's coaching staff has yet to be announced, but Van Nistelrooy, 48, will not be among them.