Everton manager Marco Silva is fighting to save his job after Saturday’s 2-0 home defeat by Norwich.
The loss increased concerns behind the scenes and Silva’s position is set to be discussed between major shareholder Farhad Moshiri and other directors.
David Moyes, who spent 11 years as Everton boss before joining Manchester United in 2013, has been discussed as a potential interim option.
The Toffees have lost seven of their 13 league games this season.
Silva may yet get a stay of execution due to a lack of suitable replacements.
Moshiri may be reluctant to make the change yet after the experience of sacking Ronald Koeman without a replacement lined up in October 2017.
Everton’s third home loss of the campaign, and their sixth in their last nine league games, saw them slip to 15th place, while Norwich, who were bottom of the Premier League at kick-off, moved up to 18th.
A number of fans sang “sacked in the morning” at the end of the match.
Everton face a tricky run over the next few weeks, with matches against Leicester in the league and Carabao Cup quarter-finals, plus league games against Liverpool, Chelsea, Manchester United, Arsenal and Manchester City.
“It is not the moment to talk about individual positions,” Silva, 42, said after the game. “We have to look what is best for us as a club and for myself and the players as well – but always the club has to be at the top.
“If you are really disappointed with the afternoon I can imagine they [fans] are as well and they have the reaction to the manager and the players.
“When you lose a match, the first person they look to is the manager. Football is like that.
“The message is I respect what is their feeling, for sure. It is not the first time they felt the way they felt this afternoon.”
Asked if he would be speaking to Moshiri, the Portuguese added: “It is possible. Normally we do that. I cannot say to you 100% sure but [it is] normally something we do.”
Silva replaced Sam Allardyce at Goodison Park in May 2018 and has won 25 and lost 22 of his 58 games in charge.
The former Hull City and Watford manager was brought in with the hope of his side playing more attractive football and was backed with almost £90m of new signings in the summer of 2018.
The Toffees finished eighth last season in Silva’s first campaign but, after spending more than £100m on new players in the summer, they have won just four league games this season