The 63-year-old reveals that the Gunners were looking into the possibility of buying the French defender before he moved to the Spanish champions in the summer of 2011
The 19-year-old moved to the Santiago Bernabeu from Ligue 1 side Lens in the summer of 2011 and has become a top performer for the Spanish champions since, earning his first international cap for France in the process.
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"He was at Lens and we might well have caught him there," the Gunners boss explained to Eurosport. "You have to ask yourself why this player is not playing for Arsenal.
"I'm happy for him because he's carving out a role at one of the world's best clubs. [Madrid coach Jose] Mourinho has chosen him to step in.
"It was a risk for Real Madrid to sign him at his age but, when you have such talent, you can overcome everything. His next challenge is managing the increased media exposure on him, especially now he is in the French national side."
Varane has made 20 appearances for Real Madrid this season, scoring once – his side's only goal in their 1-1 first-leg draw in the semi-final of the Copa del Rey against Barcelona.