Historically the Hammers' managerial recruitment policy revolved around a previous, if sometimes tenuous, connection to the club. But with owners David Sullivan and David Gold aiming for European football in the not too distant future and the move to the 54,000 capacity Olympic Stadium just over a season away, the focus appears to have shifted to some of the top managers in the European game.
But should Allardyce depart, can the club really attract a managerial big gun as their 15th boss?
One name on the supposed shortlist of potential Allardyce replacements that does have those Upton Park connections is Slaven Bilic, the former Irons centre back and cult hero. The Besiktas boss has been frequently linked to an Upton Park return, most recently by the Daily Mail, and seems a plausible choice, particularly since coming under fire from his club's famously vociferous fans after their exit from the Europa League.
It is difficult to gauge Bilic's achievements in Turkey, though, as Besiktas, considered the second biggest club in the country, currently sit third in the Super Lig behind Fenerbahce and table topping bitter rivals Galatasaray.
Interestingly for West Ham fans, the no-nonsense Croatian boasts a win percentage of 56.13% during his 212 games as a manager so far in his career, while Big Sam has won 39.50% of his 914 matches as a boss.
So what of the Benitez link? According to the London Evening Standard's Ken Dyer, 'West Ham would be a realistic option for the 54-year-old'.
His career has been laden with trophies and he added another two to the cabinet with Napoli in the form of the Coppa Italia and Supercoppa. But a side which had become accustomed to battling for the Serie A title and Champions League places in recent years currently find themselves languishing in sixth with little hope of dining at Europe's top table next season.
The feeling among some Hammers fans is that, like Alan Curbishley before him, the Spaniard once described as the 'luckiest manager ever' by Sir Alex Ferguson is simply too dour and does not play attacking football home and away true to the club's roots.
But the former Liverpool, Chelsea and Inter Milan manager's statistics speak for themselves. From an almost identical number of games as the man he could replace, Benitez has a remarkable 464 wins from 912 games with a ratio of 50.88%. Perhaps the more striking statistic, though, is that his sides have amassed a positive goal difference of 579.
The third of the big four on the reported shortlist is 59-year-old Argentine Marcelo Bielsa, the current Marseille boss. The former Argentina and Chile coach is something of a footballing eccentric and is famous for deploying a 3-3-3-1 formation with an aggressive pressing style.
He has led Marseille to third in Ligue 1 this season with an outside chance of beating rivals Paris St Germain to the league title. He boasts a winning percentage of 49.08 in his career so far with 134 victories from 273 games as a manager.
Former Manchester United, Everton and Preston North End boss David Moyes is another being heavily linked with Upton Park should he return to the Premier League. Fears that his playing style is too similar to the man he could replace niggle with some West Ham fans as does his perceived dour character.
His win percentage stands at 44.48 from 825 games and he has led new club Real Sociedad to midtable in La Liga. He has been tipped by Allardyce himself to bounce back from his Red Devils disappointment, but could it be in Big Sam's seat at the Boleyn?
So what of the case for sticking with Big Sam? There is no denying Allardyce divides opinion at West Ham. But while a noisy section of fans have made their feelings clear periodically throughout his tenure, he still has support from some of the Upton Park faithful who feel the club is progressing steadily under his stewardship and playing better football than they are often credited for.
The owners - and Allardyce himself - have always insisted they would talk contracts at the end of the season, as is club policy. Ironically by that time Big Sam could be in an even better bargaining position as the club still harbours genuine hopes of a Europa League place via the Fair Play route.
Many fans would argue Allardyce was the bitter medicine the club had needed for a long time and continues to prove he is the safe pair of hands to help them reach the Olympic Stadium in good shape come the 2016-17 season. But others want to start aiming higher and his refusal to pander to the romantic notions of some Hammers and their ideals on how the game should be played, home and away, means he will never be truly accepted by everyone in the stands whatever happens come May.