Everton will begin contract talks with Carlo Ancelotti after he was sacked as Napoli manager on Tuesday evening following their 4-0 victory over KRC Genk.
Former Everton boss David Moyes could still return to Goodison Park in an interim role, while a new permanent manager is put in place.
Arsenal are also considering Ancelotti, who managed Napoli for 19 months, to succeed Unai Emery.
Napoli announced the decision to dismiss Ancelotti an hour after he led the club to the knockout stages of the Champions League with a thumping home win against Genk, ending a nine-match run in all competitions without victory.
A Napoli club statement read: “SSC Napoli has decided to revoke the role of first-team coach from Mr Carlo Ancelotti.
“The rapport of friendship, admiration and reciprocal respect between the club, its president (Aurelio De Laurentiis) and Carlo Ancelotti remain intact.”
Vitor Pereira, who was viewed as the leading candidate at Everton, pulled out of the process to become the successor to Marco Silva earlier on Tuesday.
Duncan Ferguson is currently Everton’s interim manager and won an emotional first game in charge, beating Chelsea 3-1 at Goodison Park.
Sky in Italy reported on Tuesday former AC Milan manager Gennaro Gattuso is the leading candidate to take over at Napoli, and is set to sign a provisional six-month deal.
They are also understood to have enquired about Lazio boss Simone Inzaghi, who has led the club to third place in Serie A.
However, he is believed to be happy to stay at Lazio – although he would be interested in moving to England in the long-term.
Chelsea head coach Frank Lampard says his former boss Ancelotti is good enough to manage anywhere.
Speaking after the 2-1 win over Lille, Lampard was asked if the Italian could return to the Premier League.
He said: “I’ve got huge respect for him. I’m sorry to hear that [he has been sacked].
“I know it has been a tough situation for him lately. I saw his interview before the game and it was typically classy in what seemed like a tough time for him. He’s always handled himself brilliantly.
“I think he can manage anywhere in the world at the top level, of course.”
-Report by skysports