The Dutchman, 46, joined the Spanish side from Manchester United in 2006 after a five-year spell at Old Trafford.
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He spent four years at the Santiago Bernabeu, where he scored 64 goals in 96 appearances.
But Van Nistelrooy has since admitted that leaving Real Madrid for German side Hamberger SV in 2010 remains one of his biggest regrets.
When speaking to Gary Neville for an episode of The Overlap, he said: “Pellegrini was our coach and he signed Karim Benzema, Kaká and Ronaldo.
“There was no place for me anymore. I accepted it, also because I was 33 years old.
“I wanted to go to the World Cup in 2010, so I decided to go to Hamburg. I made that decision too quickly.
“If I look back, I shouldn’t have left Madrid, it was the biggest mistake of my career.
“Also, it was not the right time for my family to leave either.”
Van Nistelrooy won two La Liga titles and two Spanish Super Cups during his time with Real Madrid.
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But arguably the most successful period of his career came during his time with Man Utd.
He scored 150 goals in 219 appearances for the Red Devils and won a Premier League title, an FA Cup and a League Cup.
In the interview with his former United teammate, Van Nistelrooy was also full of praise for legendary manager Sir Alex Ferguson.
He added: “Alex Ferguson is the best coach I’ve ever had. I spent five years with him at United.
“I had never been with any other coach for so long. When you see the legacy he left at United…he is by far the best.”
The Dutchman retired from professional football in 2012 and switched to a career in management.
He is now in charge of PSV Eindhoven.