Ferguson may not have signed his man back then but the Frenchman finally arrived at the Theatre of Dreams for £42m this summer.
"It was a special moment for me and my family," Varane told Sky Sports. "It's amazing to meet a person like him at 18. You know, after that, it's your destiny. Ten years in Madrid and now I'm here.
"This is a new challenge for me. A different competition, a different mentality, a different atmosphere. It's all new for me but I've enjoyed every day so far.
"It's a big challenge to get Manchester United back to the top but I feel people want to win, people want to do great things with this club, and that's a big motivation for me.
Varane's move was rather overshadowed by United's sensational swoop for Cristiano Ronaldo but the 28-year-old holds no grudges as he relishes the reunion with his former Madrid team-mate.
"I think he is the best example in the world in terms of work ethic and winning mentality," says Varane, who shared a dressing room with Ronaldo for seven seasons at Real Madrid.
"Playing with this type of player, you improve every day. If he is still playing to such a high level at his age, it's because his work is amazing. I'm very happy to play with him."
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