That has put manager Allardyce back under pressure, even with the Hammers pushing for a place in the Europa League - something few fans could've expected at the end of last season.
However, rumours are circling over 'Big Sam' and his future at Upton Park, with his contract set to expire this summer; and co-chairman David Sullivan told the London Evening Standard that there will no talks over a new deal until the end of the season.
It seems like West Ham are waiting to see just how far Allardyce can take them this season, but speculation is already starting to gather pace over a possible replacement for the former Blackburn Rovers boss.
The Telegraph believe that former Manchester United boss David Moyes is on their wishlist, with the Scot currently managing in Spain with Real Sociedad, but so is the aforementioned Bilic.
The Croatian, 46, is currently managing Turkish side Besiktas, and is preparing his side to face Liverpool in the Europa League this week.
As a player, Bilic made 48 appearances for West Ham, playing as a defender for the club in the late 90's before moves to Everton and Hajduk Split.
Best known for his work with the Croatian national team, Bilic currently has Besiktas sitting top of the Turkish Super Lig, having lost just three games all season.
Earlier this term, Bilic admitted that he would be interested in a move back to the Premier League at some stage in his career - and given his affinity with West Ham, he could be the ideal replacement for Allardyce.