Carlo Ancelotti was sacked by Napoli shortly after guiding the Serie A club to the last 16 of the Champions League.
Napoli confirmed the news after their 4-0 victory over Genk, which was their first win in 10 matches in all competitions.
SSC Napoli has taken the decision to part ways with first-team coach Carlo Ancelotti.
The friendship and mutual respect between the club, President Aurelio De Laurentiis and Carlo Ancelotti remain intact.
— Official SSC Napoli (@en_sscnapoli) December 10, 2019
Arsenal and Everton could move for Ancelotti, who won a Premier League and FA Cup Double with Chelsea in 2010.
Vitor Pereira, who was viewed as the leading candidate at Everton, has pulled out of the process to take over at Goodison Park.
Mikel Arteta is the favourite to succeed Unai Emery at Arsenal but that could change with Ancelotti now a more realistic option.
The 60-year-old is one of only three managers to win three European Cups/Champions Leagues and has also won domestic titles with AC Milan, Chelsea, Paris St-Germain and Bayern Munich.
Ancelotti replaced Maurizio Sarri at Napoli in July 2018 and finished second last season, 11 points behind Serie A winners Juventus.
Napoli beat Liverpool 2-0 in their opening group game of this Champions League campaign and that is the only defeat Jurgen Klopp's side have suffered this season.
However, Napoli are currently seventh in Serie A, 17 points behind league leaders Inter Milan.
Another major issue for Ancelotti was down to problems off the pitch, which started last month.
The manager and Napoli players were in a high-profile dispute with president Aurelio de Laurentiis following a 1-1 draw with Red Bull Salzburg in the Champions League on November 5.
De Laurentiis ordered the team to attend a week-long training camp but Ancelotti and his players all returned home.
The club threatened legal action against the squad, while holding Ancelotti solely responsible.