According to 'Sky Sports', Napoli are holding out for £25m for the striker, who has been at the club for just over 18 months.
Since joining Napoli, Gabbiadini has scored 20 goals in 61 appearances for the Naples club.
The Toffees have already made five signings this summer and are hoping to bring in the Napoli man before the transfer deadline.
Everton have had an impressive start to the season, taking seven points from their three league games.