The Spaniard joined Los Blancos from Manchester City in January 2019 and made 11 appearances for the capital giants in the second half of the 2018-19 campaign.
Diaz has found it difficult to earn minutes for Zinedine Zidane's side this season, though, making just nine appearances in all competitions.
The 20-year-old could allegedly be allowed to leave the Bernabeu on loan next season, and according to Mundo Deportivo, Betis are in the running to secure his signature.
Betis will be managed by former Manchester City and West Ham United boss Manuel Pellegrini next term, and the 66-year-old will reportedly be backed in the market this summer.
Diaz appeared as a late substitute as Madrid took another step towards winning La Liga by beating Alaves 2-0 on Friday night. body check tags ::