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 coach Roberto Martinez was subject of an initial approach but 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.