Portuguese coach Vitor Pereira is on Everton's radar as owner Farhad Moshiri continues the search for a successor to sacked manager Rafael Benitez.
Pereira, 53, has been linked with the club on several occasions and is currently out of work after leaving Fenerbahce in December.
Belgium's Roberto Martinez was subject of an initial approach but Everton were snubbed by the country's FA.
Derby boss and ex-Everton striker Wayne Rooney is also under consideration.
The Goodison Park club are understood to have spoken to former Chelsea boss Frank Lampard following the rebuffed approach for Martinez, who was sacked by Moshiri in 2016.
Italy's World Cup-winning captain Fabio Cannavaro is another name who has been mentioned as a possible candidate.
Duncan Ferguson has again assumed caretaker control and was in charge for Saturday's 1-0 home defeat to Aston Villa, which left Everton in 16th place in the Premier League with only one win in their last 14 league games.
Everton spoke to Pereira before Carlo Ancelotti was appointed in 2019 but he signed a lucrative new deal at Shanghai SIPG in China.