The 60-year-old's contract is up this summer. But the Hammers should be wary of some of those linked with taking his place at Upton Park.
According to sports betting website Oddschecker, there is no shortage of candidates to replace Sam Allardyce next season should West Ham United choose not to renew the 60-year-old's contract this summer.
Among the leaders, though, there are some the east London side should avoid at all costs...
David Moyes, for one, is one of the leading contenders to replace Allardyce at Upton Park. But a move would make little sense.
The main gripe West Ham fans have had with Allardyce's sides has been their style of play and lack of attacking instinct. Moyes is made in the same mould.
At the end of the day, he even turned Manchester United into a defensive side.
Talk of him rejuvenating his career at Real Sociedad, meanwhile, is premature. Sure, he beat Barcelona in a one-off game - but where are they in the La Liga table? That's right: 12th.
At Everton, Moyes was the same - triumphing against big teams because that's what he specialises in: sitting back and soaking up the pressure. That's not what West Ham fans want - otherwise Allardyce would be A-okay.
Another man among the favourites with the bookies, a Gus Poyet appointment would be a real risk for West Ham.
Allardyce may be a subject of supporter criticism but at least there is no danger of relegation under the current coach. Even when there was last season, he steered the Hammers clear as he has done many times before in his career.
Poyet, though, fell out with fans at Sunderland and had them near the relegation zone throughout his time at the Stadium of Light. The Uruguayan blamed a lack of transfer funds for his failings but the West Ham owners would only have his word for that...
Also a man with a huge risk factor. Marcelo Bielsa may be every football hipster's dream but there has been little recently to suggest he can sustain success as a manager rather than as a tactical theorist.
His Athletic Bilbao side were exceptional for a season - then things fell apart. Bielsa's Marseille side are also currently fifth is Ligue 1 and the Argentine, crucially, has no Premier League experience.
In his own words from two days ago, according to Goal.com:
"I must find solutions. Before each game, I hope we go down the correct path but, in the last two defeats, there has been little in evidence to defend my management.
"I cannot absolve myself of my responsibilities. I feel shame for this run of defeats more than any other feeling. Are Marseille in crisis? Of course we are."
At least he's honest - but the man for West Ham? It doesn't look like it.