Everton chairman Bill Kenwright is reportedly fearful that the club could be embroiled in a relegation scrap and has targeted Sam Allardyce to save them from trouble.
The Toffees are currently inside the bottom three after a disappointing run of results, leading to the sacking of manager Ronald Koeman earlier this week.
According to The Sun, Everton chief Kenwright is concerned about his side's short-term prospects and wants Allardyce to steady the ship by succeeding Koeman in the Goodison Park dugout.
Owner Farhad Moshiri is said to prefer a foreign manager, however, with Carlo Ancelotti his top choice to take the club forward during this turbulent spell.
Everton can climb out of the relegation zone with a point against Leicester City at the King Power Stadium on Sunday afternoon.