Marca says Real Madrid have offered an extension beyond next season.
But the stalwart is hesitant to sign a new contract and end his career at Real Madrid.
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Several clubs are ready to act if Nacho decides to leave this summer.
The 34-year-old was already set to leave after last season, but changed his mind at the last minute.
The Real Madrid captain still has Carlo Ancelotti's trust, but he could leave seeking more minutes.
When David Alaba and Eder Milito are fully fit, the competition will be fierce, especially with Antonio Rdiger also available.