Julen Lopetegui is likely to be sacked if they lose at home to Wolverhampton Wanders on Monday night and the Hammers are considering making a short-term appointment to steer them away from any threat of relegation.
As reported by talkSPORT on Sunday, former Juventus boss Max Allegri has also held talks with the London Stadium hierarchy.
However he is reluctant to take a job in the Premier League mid-season and would only take it next summer.
Former Brighton manager Potter has been out of work since being axed by Chelsea in April last year.
He managed 31 Blues games, losing 11 - leaving Chelsea in 11th place in the Premier League.
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But he is now ready to return to the dugout for the right opportunity.
Potter has also been tipped to take over from under pressure Ange Postecoglou at Tottenham, with the Spurs boss losing 4-3 to Chelsea on Sunday off the back of a 1-0 defeat at Bournemouth in mid-week.
Gary O'Neil's side sit second from bottom, four points from safety.
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The Hammers, meanwhile, are 14th, six points from the relegation zone.
West Ham have won just once in their last five Premier League fixtures - a 2-0 win at Newcastle.
Further pressure was dumped on Lopetegui after his side's 3-1 defeat away at Leicester last Tuesday.
The Spaniard has only been in charge since May when he took over from David Moyes at the end of last season.
talkSPORT understands former boss Moyes is open to a shock third spell at West Ham should his successor get the chop.
The 61-year-old has taken charge of 261 matches across his two previous tenures with the east London club.
Moyes - who won the Europa Conference League with the Hammers in 2023 - agreed to depart at the end of last season.
He had come under increasing pressure after a poor run of results that saw him win just one game in 10 at the time of his departure announcement.
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Moyes later revealed he had been offered a new deal earlier in the campaign before it was rescinded by owner David Sullivan.