The Italian has been out of work since leaving Tottenham in March but has reportedly been contacted by the Serie A giants as they consider their options.
Rudi Garcia has struggled since Luciano Spalletti left the club this summer following an historic title win last season.
The Serie A champions sit fifth in the table and were beaten by Fiorentina on Sunday, condemning them to their fourth defeat in eight games.
Roma have also been touted as potential landing spot for Conte after a difficult start for old rival Jose Mourinho.
Conte left Spurs under a cloud earlier this year after a fiery outburst following a 3-3 draw with Southampton. There was a belief the former Chelsea manager had lost the dressing room at that point, during a difficult time in his personal life.
The 54-year-old endured a horrendous year, losing three close friends including Spurs fitness coach Gian Piero Ventrone in October, before he underwent emergency gallbladder surgery in February.
Having returned to Italy, Conte believes he made a “clear choice” in where his career goes from this point.
Asked specifically about a potential move to Napoli while playing in a commemorative match celebrating the Agnelli family’s 100th anniversary owning Juventus he said: “For now I’m enjoying my family, I made a clear choice when I left England.
“You know that many things can happen along the way. Going to Naples? We must always have great respect so let us enjoy this evening.”
