The versatile defenders is a target for three of the Italian top flight’s leading clubs – Roma, Napoli and Milan, according to the report.
The 30-year old is reportedly unhappy with a reduced role as back up to Sergio Ramos and Raphael Varane, with last summer’s signing Eder Militao now ahead in the pecking order in Madrid.
Indeed, Nacho accumulated just 685 minutes of action last season spread across 10 matches and he is now keen for more first-team football elsewhere.
Meetings between his representatives are already said to have taken place in Italy with the possibility of a transfer gathering pace.
Napoli are only likely to make a move should Kalidou Koulibaly leave this summer and whilst Roma and Milan have not yet made an official bid, they are expected to.