Carlo Ancelotti has held talks with Napoli's president in Rome about becoming their new manager, according to Sky in Italy.
The former Chelsea, Real Madrid and Bayern Munich boss looks set to succeed Maurizio Sarri, who hinted on Sunday he was leaving the club.
"Everything in life ends and it is better to finish things after writing a beautiful story," Sarri said after Napoli's 2-1 win over Crotone, which saw them end the season with 91 points, four behind Serie A champions Juventus.
Sarri reportedly met with representatives of Zenit St Petersburg last week while Chelsea have been also linked with the 59-year-old.
Ancelotti has been out of management since he was sacked by Bayern last September, while his last job in Italian football was with AC Milan, who he left in 2009 to become Chelsea boss.
Napoli have twice finished as runners-up to Juventus in the past three seasons. Their last league title success was in 1990.