The midfielder is 34 years old, but has been a sensation since joining Juventus on a free transfer in the summer of 2011, winning two consecutive Italian titles.
He also impressed in Brazil this summer and earned praise from many members of the Spain squad.
According to reports in several Spanish media outlets, Los Blancos have named Pirlo as a potential transfer target under new Coach Ancelotti.
It would be a reunion for the pair, who worked together for several years at Milan with great success, developing his deep playmaker role.
However, it is highly unlikely that Juventus would release one of their top stars, even if the idea of moving to Real Madrid at his age would be intriguing.
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