Fati, 23, spent last season on loan with the Principality club, scoring 12 goals in his 30 games across all competitions.
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Monaco are expected to make the move permanent by activating the €11 million option to buy clause included in the deal.
According to Mundo Deportivo, the club had a meeting with Jorge Mendes, agent of Casado, over a potential move.
Casado, 22, is likely to leave Barcelona this summer as they seek funds for their summer spending spree, with several top European clubs interested.