The board are reported to have felt there was no other option after the club found itself in the relegation places.
Now the search for their next manager is underway and the Toffees are understood to have identified two main targets.
Pereira was reported to have impressed the Everton board with his knowledge of the game, but he lost out to Roberto Martinez in the end.
The Portuguese manager has won titles in his homeland with Porto, as well as Turkey with Fenerbahce, and now China as well.
He is believed to be one of the highest-paid coaches in world football, earning an estimated £30m per-year in Shanghai.
Another name reportedly in contention for the Goodison hot-seat is Italian veteran coach Carlo Ancelotti.
The Daily Mail's North West reporter Dominic King tweeted saying Ancelotti has joined Pereira and ex-boss Moyes in the mix.
Vitor Perreira joined by Carlo Ancelotti on Everton’s managerial shortlist. David Moyes also an option but the fact he has not been appointed yet while freely available shows some within club have doubts. Ancelotti also in Arsenal’s thinking.— Dominic King (@DominicKing_DM) December 6, 2019
Ancelotti's position at Napoli is believed to be under severe pressure and he may become a free-agent before long.
The 60-year-old has won numerous titles in Italy, Spain and England - plus three Champions Leagues.
A potential stumbling block for Everton with regard to Ancelotti is that Arsenal are also interested in him filling their vacant head coach position.
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