Potter is becoming under increasing pressure at West Ham after defeat at home to Crystal Palace.
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Palace won 2-1 at London stadium on Saturday as thousands of fans staged a protest march against the board before kickoff.
BBC Sport says internal discussion are now being held about Potter's position and potential replacements.
Former Wolves manager Gary O'Neil, a former Hammers midfielder, is being considered, as his ex-West Ham boss Slaven Bilic. Both men are free agents.
Potter has taken charge of 25 matches since his appointment - winning just six times.