The 25-year-old Italy forward has been linked with a move away from the Partenopei as several Premier League clubs have expressed an interest in signing him.
However, Gabbiadini stayed put and appeared on course to sign a new contract extension with the club.
But he has struggled so far this season with just one goal scored in six starts and has found it difficult to fit into Maurizio Sarri’s 4-3-3 system.
Reports in Italy claim Milan have been keeping tabs on the player's situation and could pounce should they decide to offload Carlos Bacca in January.
The Rossoneri are looking to complete a sale to Chinese investors but, with that deal nowhere in sight, coach Vincenzo Montella could look to offload the 30 million euros-rated Bacca and sign Gabbiadini, with money left over to bring in more new faces.