Calhanoglu currently wants higher wages than Milan are offering, with the Turkish international's contract ending next summer.
Diaz has impressed so far this season, being seen as a direct replacement to Calhanoglu, scoring three goals and providing one assist so far this season.
Whilst Calhanoglu has been one of the best players in the team ever since Stefano Pioli took over, he often struggles for consistency.
Pietro Mazzarra of MilanNews.it has stated that "Pioli has a very valid alternative [to Calhanoglu] in Brahim Diaz, who wants to do well and, from what emerges, also to stay at Milan."
The site has also previously stated that Real Madrid are willing to sell the youngster for €25 million, with Milan showing plenty of interest in signing him permanently once the loan deal expires.
The former Manchester City midfielder joined Real Madrid in June 2019, but struggled to nail down a spot in the first-team during his time in Spain, and he has settled very quickly in Italy.
Calhanoglu is currently pushing for higher wages, but is also keen on a move away from the club, with plenty of sides interested in his signature, including Manchester United, Juventus and Atletico Madrid.