Brahim Diaz was brought on loan from Real Madrid in the previous transfer market window and since then he managed to show some of his qualities which made the Rossoneri management be convinced of him.
According to Marca (via route1futbol on Twitter) AC Milan intends to speak with Real Madrid to extend Brahim Diaz' stay in Italy. They could either present a cash offer to sign the player permanently or negotiating a loan extension for the 2021/22 season.
It was reported yesterday as well by Fabrizio Romano that Milan will be looking to keep the player, which you can read here.