Milan have struggled this season despite a heavy spending spree in the summer and it resulted in Vincenzo Montella being relieved of his duties.
Gennaro Gattuso is now at the helm and will be looking to bring in players to inject new life into his side, and Ceballos is a reported target.
The 21-year-old only arrived at the Bernabeu in the summer when signing from Real Betis, but he has failed to establish himself in the Los Blancos side despite them struggling to hit form this season.
That has kicked off suggestions in Spain that Real boss Zinedine Zidane did not want to sign Ceballos in the summer, and the transfer was the wish of Florentino Perez.
Either way Ceballos wants regular first-team football, after making just two league starts this season, and is willing to move away from the Bernabeu in the new year to get it.
Milan are keen but will face strong competition for his signature as English Premier League clubs Arsenal and Tottenham are also said to be interested.