Andoni Iraola has also emerged as an option under consideration by president Aurelio De Laurentiis.
Conte confirmed his exit at a press conference on Sunday following the club's final Serie A fixture against Udinese, which Napoli won 1-0. The Italian said it was his own decision, made a month ago, and that he would forgo part of his severance package. He leaves with one year remaining on his contract after Napoli won the Scudetto last season and finished second this term, 11 points behind champions Inter Milan.
De Laurentiis's first choice was Maurizio Sarri, whose situation at Lazio appeared to be heading toward a departure following a difficult season. However, Sarri is expected to choose Atalanta, where he would reunite with sporting director Cristiano Giuntoli, over a return to the club where he also won the Scudetto in 2018.
With Sarri off the table, attention has turned primarily to Allegri, whose future at AC Milan is in doubt after a catastrophic end to their season — they failed to qualify for the Champions League after losing 2-1 at home to Cagliari on the final day. Allegri is contracted at Milan until 2027 but his position there is far from secure.
Italiano, currently at Bologna, has hinted he may also move on.
"There is a chance I won't stay — I can't deny that," he told La Repubblica. "I want to return to European football. Bologna has the right philosophy, but I have to be transparent with the fans."
Iraola leaves Bournemouth after guiding them to a sixth-place Premier League finish. He is one of the most sought-after coaches in Europe following his work on the south coast, with Bayer Leverkusen and Liverpool also monitoring his availability.
De Laurentiis briefly addressed the coaching situation at Sunday's press conference: "We have a strong squad and many players returning. They perhaps had shortcomings for Conte's style of play, but they might fit well under a new coach."