The Croatian midfielder's deal expires in June next year and Mundo Deportivo reports the 35-year-old is keen on extending his contract with Zinedine Zidane's side.
However, the La Liga champions will not be rushed into making a decision on the former Tottenham star, who joined Madrid from the north London side in the summer of 2012.
Modric would be willing to accept a lower wage as part of any new deal given that he is coming towards the end of his career.
But there will reportedly be no problem on his part if he is asked to step aside and say his goodbyes to his team-mates if and when the club decide against a contract extension.
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