According to AS.com, the Rossoneri have already made contact with the player, hoping to conclude the deal quickly whilst emphasising that he is one of the club's top transfer priorities.
Ceballos, who was signed by Real Madrid from Real Betis for approximately £18m last summer, has only made 12 league appearances for the Spanish side due to tough competition from quality players including Casemiro, Toni Kroos and Luka Modric.
In his time with Los Blancos, Ceballos has only managed to score a paltry two goals with no assists, failing to impress the Madrid faithful and subsequently finding himself on the bench at the Bernabeu.
Such a poor record has prompted rumours that the creative 21-year-old is likely to be interested in moving to another European side to resurrect his young career.
The Spaniard will also be keen to potentially stake his claim as an international player, having already been named player of the tournament for the Spanish under-21 side at the European Under-21 Championships in 2017 and being regarded as one of the more promising young players in European football.
AC Milan are reported to be getting their transfer business completed early this summer, with reports suggesting that they are hoping to secure Alvaro Morata, Radamel Falcao or Simone Zaza to boost their front line. The club are also pinning down their star players, with the club looking to keep successful Italian striker Patrick Cutrone on a new 5-year deal.