Everton owner Farhad Moshiri wants to hire former Leeds United boss Marcelo Bielsa.
The Toffees have parted company with coach Frank Lampard, dismissing him after a string of significant defeats.
Everton are in the Premier League relegation zone and have only won three games all season.
Per The Mirror, Bielsa is the favourite for the job as he is Moshiri's ideal pick.
However, the Argentine is known to have qualms about taking jobs where he is not fully backed, and may not be willing to sign up for a club on the verge of going down.
Other candidates include Sean Dyche, Sam Allardyce, Duncan Ferguson, and Wayne Rooney.