Spanish media channel Cadena Ser reports the Rossoneri are keen on the Dutchman as Leonardo seeks to strengthen the left flank.
Drenthe has been peripheral to Manuel Pellegrini's plans at the Bernabeu this season, and voices surrounding the club suggest he could leave.
President Florentino Perez is eager to claw back some of the cash he spent during the summer, and Drenthe is said to be on the sales list. He is valued at around €6 million, and he has also been linked with Fiorentina and Juventus.
Milan have not confirmed an intent for Drenthe. However, vice-president Adriano Galliani did suggest the club would retrench in the winter transfer market, claiming that David Beckham would be the only arrival in January.
"I have never spoken about buying players - only David Beckham will arrive in January, no-one else," Galliani told Sky Sport Italia last month.
Salvatore Landolina, Goal.com