Silva had been hoping to turn around the slide with the Toffees, but their loss against Norwich City at the weekend puts him on the brink.
The Blues suffered a 2-0 defeat at home to the newly promoted side, which may mean that Silva's position is beyond repair.
Chairman Bill Kenwright and director of football Marcel Brands were involved in discussions with the club's majority shareholder Farhad Moshiri at the weekend.
Moshiri has always given his support to Silva, but recent results are leading everyone at the club to question the Portuguese manager's future.
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