Diaz is back at the Bernabeu after ending his three-year loan spell at AC Milan with his most productive season to date.
The 24-year-old contributed to 14 goals as Milan sealed a top-four finish in Serie A and reached the semi-finals of the Champions League.
The Spaniard also featured regularly during the 2021-22 season, when the Rossoneri were crowned Scudetto winners for the first time in a decade.
After Milan failed to secure a permanent move for the playmaker this summer following the expiration of his loan deal, CalcioMercato claims Italian champions Napoli also submitted an offer to try to lure Diaz back to Serie A.
The Partenopei are in danger of losing some important midfield assets from their title-winning squad, and a potentially underwhelming season could see them struggle to hold on to certain players.
Piotr Zielinski is out of contract next summer, and Elif Elmas has been subject to rumours of a move away, given his lack of starts since joining the club.
The report states Real Madrid knocked back any advances from other clubs though, stating they wanted to keep him at the club this season.
Diaz's first 18 months at the Bernabeu saw him feature just 21 times, many of which were as a substitute, before his eventual loan move to Milan.
However, on his return, manager Carlo Ancelotti has utilised the midfielder much more often, with 13 appearances across La Liga and the Champions League in the opening months of campaign.
Diaz has also shown his ability, scoring in home wins over Las Palmas, Braga and Granada, starting in four of the side's last five games.
That may give the player more belief that he will be involved regularly with Los Blancos, as he played a total of just 51 minutes across the club's first seven games this season, and starting only one of the opening 15.
Two of Diaz's recent starts came in La Liga, where Real currently lead the way, while he also featured against Napoli in the Champions League, as the 14-time winners are safely through to the knockouts as group winners.