Whether Allardyce will be the man at the helm in East London if they do is another matter entirely. The club has been linked with a host of top managers from across Europe after the Hammers slipped from fourth in the table at Christmas to mid-table on the back of just three wins in 2015.
The likes of experienced European managers Slaven Bilic, Rafa Benitez and Marcelo Bielsa have all been linked to the Upton Park hotseat in recent weeks.
A season in the Europa League, coupled with the emotions and expectations that go with what will be the club's final season at their historic Boleyn Ground, could potentially double the Irons' fixture schedule.
It has proved a difficult juggling act for Premier League sides in the past. Indeed West Ham's opponents this weekend, Everton, are a prime example of how the almost constant Thursday-Sunday schedule can impact on Premier League performances.
But as speculation over his future swirls around him, Big Sam - who once famously claimed he would be the boss of a top four club if his name was 'Sam Allardici' - says there is no need for the club's co-owners David Sullivan and David Gold to look elsewhere because he is the man for the job.
"Its an extremely difficult management (proposition), how we plan for that particular season," Allardyce said in Thursday's pre-match press conference.
"I've experienced it. I've done Europe.
"I know the difficulties of it, I know the backlash can be horrendous by the criticism you might get if your results in the Premier League go bad.
"But the experience for everybody is a fantastic experience."
Allardyce gave an insight into the level of professionalism he brings to the job by revealing he is already planning what the club needs to do over the summer to be ready for a campaign that would start as early as July 2, despite not knowing if he'll even still be in the job by then.
He said: "There are elements in the early stages (you need to look at). International players won't be back for a start.
"All the players that haven't quite played as much will probably be used more as well as some of the younger professionals.
"And remember this season we're probably two weeks later finishing than normal.
"You have to guard against what is going to be a very, very long season. There are well proven facts about the problems in Europe for teams that play there."
The experienced 60-year-old pressed home his case by reminding everyone how he handled a European excursion while in charge of Bolton Wanderers.
That season the Trotters got to the last 32 of the competition and finished eighth in the league.
He added: "We managed to cope admirably really. But it is extremely difficult to manage."