However, while the Hammers have the chance to go eight points clear of their next opponents, defeat would make it at least a three-horse race to progress from Group A.
Match preview
David Moyes has said on more than one occasion this season that West Ham's primary focus is the Premier League as they bid to challenge for the top six.
That said, a run of one win in five matches in England's top flight means that the Hammers also have to push as hard as possible in Europe in a bid to become mainstays in the competition as a bare minimum.
Sunday's 4-1 defeat to Aston Villa in a game where Moyes acknowledged that his players had been outclassed left West Ham in ninth position in the table, six points adrift of the top four.
On a positive note, West Ham have started their continental campaign in perfect fashion, coming from behind to defeat Backa Topola and seeing off Freiburg on away territory in what was theoretically their toughest game on paper.
West Ham have conceded goals immediately after half time on both occasions, something which Moyes will want to eradicate, but the Scot knows that West Ham will remain in the boxseat for a last-16 spot with another maximum return on their travels.
From the perspective of Olympiacos, their only defeat in all competitions in 2023-24 came at the hands of Freiburg, who beat them 3-2 at the Karaiskakis Stadium.
Nevertheless, they hold a two-point lead with a game in hand at the top of the Greece top flight, collecting 19 points from a possible 21.
Sunday's showdown with Panathinaikos ended up being abandoned due to a firework striking an away player, and Olympiacos will be eager to avoid further crowd trouble on Thursday.
With a 2-2 draw being posted at Backa Topola in a game where Olympiacos led 2-0, Diego Martinez knows that the stakes will be raised if his side cannot deliver against West Ham.
That said, a total of 14 goals have been scored in their last 410 minutes of football in all competitions, highlighting the threat that they pose to the reigning Europa Conference League champions.
Olympiacos Europa League form:
W
D
W
W
L
D
Olympiacos form (all competitions):
D
L
W
W
W
D
West Ham United Europa League form:
W
W
West Ham United form (all competitions):
L
W
W
W
D
L
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Team News
Olympiacos will be forced into making at least one change with defender Andreas Ndoj serving a one-match ban for his dismissal before the international break.
Ecuador international Jackson Porozo appears likely to come into the side, while Francisco Ortega is an option at left-back.
Wolverhampton Wanderers loanee Daniel Podence will start on the left wing having already scored four goals since his switch last month.
While Moyes may name a stronger European XI than usual, changes will still be made to his West Ham side, including Lukasz Fabianski featuring between the sticks.
Mohammed Kudus is certain to feature in the final third, while Michail Antonio may get the nod down the middle in place of Jarrod Bowen, who was used there versus Freiburg.
Tomas Soucek could feature ahead of Edson Alvarez in midfield having been withdrawn for the final quarter versus Villa.
Olympiacos possible starting lineup:
Paschalakis; Rodinei, Betsos, Porozo, Quini; Camara, Hezze; Masouras, Fortounis, Podence; El Kaabi
West Ham United possible starting lineup:
Fabianski; Coufal, Mavropanos, Aguerd, Kehrer; Soucek, Ward-Prowse; Kudus, Fornals, Benrahma; Antonio
We say: Olympiacos 1-2 West Ham United
Despite West Ham's ongoing European form, this has the potential to be a banana-skin for the Hammers. Olympiacos are usually a strong outfit on home soil, yet we feel that the Premier League outfit will do enough to overcome their next opponents.