Everton manager Marco Silva is fighting to save his job after Saturday's 2-0 home defeat by Norwich City.
The loss increased concerns behind the scenes at Goodison Park and it is understood major shareholder Farhad Moshiri held talks with fellow directors, including chairman Bill Kenwright and director of football Marcel Brands, after the game to discuss the growing crisis.
The 42-year-old Portuguese, who has been Everton manager since June 2018, also met with Moshiri and Brands.
Moshiri and Brands are both keen to maintain stability and support Silva, despite a furious reaction from Everton supporters towards the end of the loss, with many joining in chants of "you're getting sacked in the morning" from the travelling contingent.
It remains to be seen, however, whether their patience and support extends to Silva being in charge for next weekend's visit to second-placed Leicester City, which is then followed by a visit to Premier League leaders Liverpool in the Merseyside derby at Anfield.
Former Everton manager David Moyes and Mark Hughes have been mentioned inside the club as potential interim solutions - but Moshiri and Brands' preferred option has always been to give Silva time.
The toxic atmosphere inside Goodison Park on Saturday, with Everton fans turning on the manager, has now placed huge pressure on Silva, Moshiri and Brands.
Everton lie in 15th place despite heavy investment from Moshiri and have now lost to all three newly-promoted clubs, including home defeats by Sheffield United and Norwich City.
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.
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