The veteran is now inside the final 18 months of his current deal.
AS says he is no longer a first choice in the big games following the emergence of Fede Valverde and he will be two months away from turning 36 when his contract expires in 2021.
The midfielder had doubts of his own about continuing at Madrid after the 2018 World Cup. He decided to stay and ended adding an extra year on his contract in the year he won the Ballon d'Or.
Any contract extension will depend on how he performs between now and the end of the season and how coach Zinedine Zidane views his role within the side.