Suso joined Milan in January 2015 and enjoyed a productive season last year after eight goals and 10 assists in 41 appearances across all competitions.
The former Liverpool man has been unable to replicate that form this term and has failed to score in eight appearances in Serie A, weighing in with just one assist.
Suso did start Stefano Pioli's first game in charge of the Rossoneri as they were held to a 2-2 draw by Lecce at the weekend but his performance came in for criticism from both the fans and the media.
Reports in Italy indicate the 25-year-old is angling for an exit in the winter window