Everton will begin contract talks with Carlo Ancelotti after he was sacked as Napoli manager on Tuesday evening.
Former Everton boss David Moyes could still return to Goodison Park in an interim role, while a new permanent manager is put in place, Sky Sports News understands.
Arsenal are also considering Ancelotti, who managed Napoli for 19 months, to succeed Unai Emery, according to Sky in Italy.
Napoli announced the decision to dismiss Ancelotti an hour after he led the club to the knockout stages of the Champions League with a 4-0 home win against Genk, ending a nine-match run in all competitions without victory.
A Napoli club statement read: