The 25-year-old has been consistently linked with a move to The Hawthorns during the January transfer window after failing to hold down a regular first-team spot in Naples.
The former Sampdoria forward has only started seven Serie A matches for the Partenopei so far this term, and he has been unable to force his way into Maurizio Sarri's plans despite the prolonged absence of fellow forward Arkadiusz Milik.
Reports in Italy have now suggested that West Brom have had a €20million bid accepted for Gabbiadini and the forward could now complete a move to the Premier League.
Baggies boss Tony Pulis is believed to be keen to sign a striker, particularly if Saido Berahino leaves the club during the January transfer window, and Gabbiadini appears to be his top priority.
West Brom will have to move quickly, however, as German club Wolfsburg have also been accredited with an interest in the striker, who has made six international appearances for Italy to date.