The 34 year-old is off contract at the end of the month.
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L´Équipe says Nacho is wanted by Saudi Pro League giants Al-Ittihad.
The transfer is already being described as close - and if Nacho's move goes through, it could accelerate Real Madrid's search for a new centre-back.
Karim Benzema, N´Golo Kanté, Fabinho and Luiz Felipe are all on the books at Al-Ittihad.
Nacho has played a total of 364 competitive matches for Real Madrid. In these appearances, he has accounted for 16 goals and ten assists.