The Spanish giants are expected to bring their lengthy pursuit of the 24-year-old Tottenham star to a successful conclusion before the end of the transfer window, with their online club shop already seen to offer shirts bearing his name.
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"I think it's just the lure of Real Madrid. I can't really see him staying to be honest," Keane remarked.
"I'd like to see him stay there, maybe for one more year, but it's Real Madrid - what do you expect? He's a young lad.
"It's the same opportunity that I had going to Inter - they don't come around very, very often. I took my chance. If Gareth takes his chance, if he goes or stays, I wish him well either way."
However, despite reports that a £93 million bid had been accepted by Tottenham, the clubs remain locked in negotiations. As revealed by Goal on Wednesday, the two clubs have yet to reach a formal agreement over the proposed transfer.