Crespo, who played for the likes of Lazio, Inter Milan and AC Milan during a successful career, attended a training session with the capital outfit this week to watch Ancelotti's training methods.
"Ancelotti is an extraordinary person who gave me a lot," he told Real Madrid's official website.
"He was my coach in my first years in Europe, for two years at Parma and then Milan. You could say that is not very long when you consider how close we are.
"It's almost 20 years since we first met and it's always a pleasure to come and meet him."
It is believed that Crespo, 38, is keen to step into management.