Allardyce may have enjoyed a fairly successful season to date, but a run of one win in the last eight games has the pressure firmly on the former Blackburn boss.
With his contract set to expire this summer, Allardyce may be allowed to walk away from Upton Park as the Hammers look to illustrate the ambition of the club ahead of their move to the Olympic Stadium in 2016.
Now, with an exit looking increasingly likely, the Daily Mail believe that West Ham have put together a list of five possible candidates to replace Allardyce - and it's full of illustrious names.
Bilic is currently in charge of Besiktas, but having previously played for West Ham as a defender in the 1990's, could well be open to a return to the Premier League.
Bielsa is out of contract at Marseille at the end of this season and has hinted that he will leave the French club, whilst Laudrup is managing in Qatar with Lekhwiya - and an offer to return to English football may be too good to turn down for the former Swansea boss.
Moyes is of course working with Real Sociedad right now, rebuilding his reputation after his dismal spell as Manchester United boss, whilst former Barcelona boss Rijkaard is something of the wild card having been out of management for over two years since leaving his post as Saudi Arabia manager in 2013.
It seems that co-chairmen David Gold and David Sullivan are eyeing a big name appointment if Allardyce leaves - and the lure of the Olympic Stadium could well help them in that bid.