The former England boss will hold talks with the Merseyside club's majority owner Farhad Moshiri in the next 48 hours and is set to be told that he is no longer wanted.
Marco Silva, the former Hull and Watford boss, could replace Allardyce.
Allardyce was tasked with steering the Toffees away from relegation danger after being appointed as Ronald Koeman's successor in November.
He achieved that, leading Everton to an eighth-place finish in the Premier League, but supporters have not been impressed by the playing style.
Allardyce was booed before and after the final day defeat at West Ham on Sunday, with a section of the Everton faithful chanting for him to be sacked.