The 19-year-old is yet to agree a contract extension with the Premier League champions, with his current deal expiring at the end of the season.
He is free to negotiate pre-contract terms with any non-Premier League club starting January 1, and available on a free transfer in the summer – though Madrid may look to move for him in January itself, which would mean they negotiate a fee with City.
Diaz has risen through the ranks at City’s academy and been around the fringes of the first team since last season, making 14 appearances across competitions since then.
However, playing time has been limited, with City’s abundance of attacking midfielders leaving Diaz with a steep hill to climb to become a first-team regular.
A transfer to Madrid would mark a return to home territory for Diaz, who was born in Malaga and began his career in Malaga’s academy before moving to City in 2014.
