Allardyce is currently under increasing pressure as West Ham boss having led the team to just two wins in 2015, which is a big difference from the impressive early season form, which had seen the Hammers challenging for a place in European football.
Sunday's 2-0 defeat against Manchester City was another blow for Allardyce, and with his contract set to expire this summer, the expectation is that 'Big Sam' will depart from the Upton Park dugout at the end of the season.
The London Evening Standard recently reported that the Hammers were considering moves to appoint one of Slaven Bilic, Rafael Benitez and David Moyes with the West Ham hierarchy clearly looking to make an ambitious appointment ahead of the club's move to the Olympic Stadium in 2016.
Allardyce still has some weeks to go until a decision is made over his contract, but it seems that the West Ham players have downed tools for the season until they know who the manager next season is.
That's an idea that former Blackburn striker Jason Roberts agrees with, as the pundit told BBC - and whilst he is bound to defend Allardyce given that he played under him at Blackburn, he compared the situation to Tim Sherwood and John Carver's interim spells as Tottenham and Newcastle manager.
"It is not just the players. For most people watching the situation, myself included, it looks as if Allardyce will not be in charge next season," said Roberts. "But the way the situation has been handled has been messy and I think it has undermined West Ham's season.
"When a team of players know the manager might not be in charge for the longer term, then it is harder to motivate the group. They don't need to impress you. When he was Tottenham manager, Tim Sherwood came out with that quote about being a supply teacher, and he is exactly right. Ask Newcastle boss John Carver too. That is the problem Allardyce has to deal with at the moment," he added.
Should West Ham keep Allardyce beyond the end of this season?