Everton have approached former Arsenal manager, Unai Emery, about replacing Marco Silva, according to Sky Sports.
An informal meeting was held in London and it is thought that Emery wants more time to think about his next move, following his sack at the Emirates.
The Spaniard wants to continue improving his English as he sees England, as well as Spain and Italy, as viable options for his next job.
Everton are also believed to be keen on Shanghai SIPG boss, Vitor Pereira.
Chairman Bill Kenwright and majority shareholder Farhad Moshiri have drawn up a four-man shortlist, which includes Napoli manager Carlo Ancelotti.