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The Argentine shot-stopper celebrates his 38th birthday this September and he is currently the back-up for Kepa Arrizabalaga at Stamford Bridge.
The interest has been stemmed from Keylor Navas telling Madrid that he wants to leave the club due to being number two to Thibaut Courtois, also formerly of Chelsea, in the Spanish capital.
Andriy Lunin and Luca Zidane have also been sent out on loan by Madrid, meaning that the club would need to sign an alternative.
Caballero has played in Spain across nine seasons between Elche in the second division before joining Malaga in the top-flight in the 2010-11 campaign.
The Argentine started his career at Boca Juniors and has subsequently played in England as a back-up goalkeeper at both Manchester City and Chelsea.
