Los Blancos sold Morata to Juventus in the summer but have a buy-back option of around £25m.
Morata was looked at by Arsenal, Liverpool and Manchester United in the summer before sealing a £20m move to Serie A.
The 22-year-old has scored three goals in his last six games and has been hailed in the Italian press after his performance against AC Milan at the weekend.
Morata,22, has two full Spain caps having made his debut in November.
And according to reports in Spain Real Madrid are considering a move to bring him back to the club.
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