The Hammers are currently six points behind fourth-placed Chelsea with a game in hand, while Brighton occupy 17th position in the table, but the Seagulls have already secured another season of top-flight action.
Fulham, West Bromwich Albion and Sheffield United have now been confirmed as the three relegated teams for the 2020-21 campaign, but Brighton will not want to be the side that finishes in 17th position.
It is incredibly tight towards the bottom of the division, with only four points separating 17th-placed Brighton from 13th-placed Crystal Palace and therefore a lot of chopping and changing is expected to take place over the next three matches.
Brighton will certainly feel that they are capable of finishing as high as 13th, but there is no getting away from the fact that the Seagulls have simply not won enough matches this term, picking up maximum points in just eight of their 35 matches, while they have drawn 13 and suffered 14 defeats.
Graham Potter's side will enter this weekend's match off the back of a 2-1 defeat at Wolverhampton Wanderers last time out, while they have a difficult end to the campaign, facing Manchester City (H) and Arsenal (A) in their final two matches.
Brighton did win their last home match against Leeds United at the start of May, though, and they have actually never lost a Premier League game against West Ham, remaining unbeaten in their seven previous meetings against the capital side at this level of football.
Each of the last four fixtures between Brighton and West Ham has finished level, but the Hammers will be desperate to pick up all three points on Saturday night as they chase a top-four position entering the final straight.
Chelsea's surprise 1-0 home loss to Arsenal on Wednesday has certainly opened the door for David Moyes's side, who are currently fifth in the table, six points behind Chelsea, who have played a game more.
Liverpool will have the chance to move above West Ham on Thursday evening when they head to Manchester United, but West Ham would keep themselves in the picture with a victory in this match, and there is no question that a spot in Europe next term would be a huge success story for the Hammers.
Moyes's team have actually lost three of their last four league matches, including a damaging 1-0 home defeat to Everton last weekend, but they won their last away game at Burnley on May 3 and will now be targeting victories against Brighton, West Brom and Southampton to finish the season.
The Hammers have the second-best home record in the Premier League this season but have still managed to win eight times on their travels and will view Saturday's clash at the Amex as one of their biggest fixtures of the campaign.
Adam Lallana should be able to return to the starting XI, though, while Florin Andone is likely to be available for selection. The Seagulls could revert to a back three for this match, with Dan Burn and Ben White set to be joined by Adam Webster.
West Ham boss Moyes will provide an official update on his squad during Friday's pre-match press conference, but the early indications are that Declan Rice will be available to return from a knee injury this weekend.
Angelo Ogbonna was back in the squad against Everton and should be ready to start, while Jarrod Bowen could replace Said Benrahma to feature alongside Jesse Lingard, Pablo Fornals and Michail Antonio in attack.
Brighton & Hove Albion possible starting lineup:
Sanchez; White, Webster, Burn; Gross, Lallana, Bissouma, Moder; Mac Allister, Trossard; Welbeck
West Ham United possible starting lineup:
Fabianski; Coufal, Dawson, Ogbonna, Cresswell; Soucek, Rice; Bowen, Lingard, Fornals; Antonio
We say: Brighton & Hove Albion 1-2 West Ham United
West Ham certainly need the points more than Brighton, who are going to be missing some very important players this weekend. We are expecting a tight match at the Amex but fancy the Hammers to boost their European hopes with a narrow victory over Potter's side.
Watch the Sports Mole Football Shorts prediction for this game below: