Former AC Milan manager Gennaro Gattuso is the leading candidate to take over at Napoli if Carlo Ancelotti leaves the club.
Sky in Italy say the Serie A side are considering their options following a dismal season which has included a poor run of form and disputes between the players and club president Aurelio De Laurentiis off the pitch.
Napoli face Genk on Tuesday in the Champions League and a defeat could spell the end of Ancelotti's time in charge.
It is understood that Everton is a possible destination for the former Chelsea manager if he is sacked.
Napoli have endured a turbulent campaign so far, with the club fining players for not attending an in-season training camp following a 1-1 draw against Red Bull Salzburg in the Champions League in November. That move was then contested by world footballers' union FIFPro.
In his playing days, Gattuso spent just over a year at Rangers before going on to win two Serie A and two Champions League titles in 13 years at AC Milan - where he played under Ancelotti.
He also won the World Cup with Italy in 2006.
After spells as manager of Sion, Palermo, OFI Crete and Pisa, Gattuso returned to AC Milan to manage the U19s before taking over the first team in late 2017.
He left his role in the summer after the club narrowly missed out on a top-four finish and Champions League football.