The Daily Star is of the belief that the Spanish giants are pondering a £25million move for the England goalkeeper as they look towards the future.
Real legend Iker Casillas is no longer first choice at the Santiago Bernabeu with Carlo Ancelotti preferring Diego Lopez in goal which could prompt the Italian to make a move for Hart at the end of the season.
Hart is contracted to City until the summer of 2016 but could be lured away from the Etihad Stadium especially after he was dropped from the first team by Manuel Pellegrini earlier this campaign.
Coincidentally, 26-year old Hart is looked after by the same firm that worked with Madrid to get the £85million Gareth Bale deal over the line in September last year.
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