However, Koeman told the media on Wednesday - on the eve of their Europa League clash with French side Lyon - that he felt reassured following last Friday's chat with Moshiri.
Koeman believes he has no reason to worry about his job just yet after holding talks with Everton majority shareholder Farhad Moshiri and chairman Bill Kenwright at the club's training ground.
"He [Moshiri] was here but not only him, Bill was here and others from the board because they had not yet seen the new building at Finch Farm", Koeman said in a pre-match press conference."You speak about football of course".
"Okay, everybody knows that's a nice thing but in football, it's all about results. Until now it's full, total support from the board, yes".
Netanyahu says Israel won't tolerate Iran presence in Syria
"We are in Damascus to assert and coordinate and cooperate to confront our common enemies, the Zionists and terrorists". Israel's air force says it has struck arms convoys of the Syrian military and Hezbollah almost 100 times during the war.
It is no secret Koeman's men have struggled with injuries all season, with many facing long-term injuries, however, they recruited heavily in the summer having been provided with some much needed financial power. Most of the time the manager doesn't get time to improve the team.
Koeman hasn't lost the fanbase as a whole but he has lost a vocal part of the Goodison Park.
"We always knew we had a tough start to the season; when we play Arsenal on Sunday it will be the fifth game from nine against teams who finished in the top five of the Premier League last season". "With one point out of two matches we need a win, and especially a win at home if we are to have good a possibility to go through in this tournament".
The Blues are winless in three games and face an extremely hard test against Lyon on Thursday night with the place in the Europa League on the brink. "Depay chose Lyon, he's still young, he's always unsafe, when he's not on his level he has indivudal qualities that makes him risky, we need to control him".