Reports broke this morning in the Telegraph claiming that Allardyce had turned down a contract extension at the Boleyn Ground, but the Mail suggests that these are false.
They say that West Ham's board have still not even begun to discuss a new deal with the 60-year-old, with the club waiting until the end of the season to decide his future.
Allardyce's current deal expires in the summer and there is an increasing feeling from supporters that the club need a fresh start.
Although the experienced boss has continually improved West Ham, a poor run of form over the second part of this season could cost him his job.
The London side had looked in with a chance of claiming a European spot at the turn of the year, but a run of just three wins in 16 games across all competitions has seen them slide down the table.
The Hammers are now fighting it out to finish in the top-half and it seems that even if they achieve that it may not be enough to save Allardyce's job.