Allardyce, who has been in charge at Upton Park for almost four years, had a superb start to the season, and were challenging for a European place up until Christmas.
Since then though, it's been tough going for the Hammers. With just one win since Christmas, Allardyce is under increasing pressure to turn things around before the end of the season.
The 60-year-old was tipped to leave West Ham last summer, but the Hammers board backed him with a raft of new signings such as Aaron Cresswell, Carl Jenkinson, Alex Song, Cheikhou Kouyate, Diafra Sakho and Enner Valencia.
This time, it seems that Allardyce will be departing when his contract expires this summer, with the Daily Mail reporting that there is 'no way back' for Allardyce at West Ham - even if he can spark a good run of form before the end of the season.
That looks unlikely after Saturday's 3-0 defeat to Arsenal, and the Daily Mail report that West Ham will cut ties with Allardyce the day after West Ham's final game of the campaign against Newcastle on May 24th.
West Ham will choose not to renew Allardyce's contract when it expires in July according to the report - leaving the Hammers to look for a new manager ahead of their final season at Upton Park before they move to the Olympic Stadium in 2016.