The goalkeeper was the first choice in the Liverpool goal for the first half of last season, but lost his place to Loris karius as the campaign.
Now with the arrival of world-record signing Alisson, it means that the Belgian international is third in the pecking order for the 'Reds'.
As a reuslt, he is keen for a move away from Merseyside to try and reignite his career, and it seems as though he could do that in Italy.
Napoli lost their main goalkeeper Pepe Reina, of course formerly a Liverpool goalkeeper himself, to Milan earlier in the summer and have added Orestis Karnezis and Alex Meret to the squad since then.
Neverthless, Carlo Ancelotti is thought to want to further strengthen that department, and could look to Mignolet to do that.
This deal does not have to be done before Thursday's deadline in the English transfer window as the Italian window does not shut for another month.