The Hammers know that they will finish sixth again if they win and Manchester United drop points at Crystal Palace.
The Irons finished in the same position last year and could do so again this season if they finally beat Brighton in the Premier League.
The Seagulls have faced the Hammers nine times in the top-flight and they are unbeaten in all.
If that were to happen again, West Ham would miss out on Europa League football even if Palace did them a favour.
Meanwhile, Graham Potter's men can still finish in the top eight, which would be some achievement from Brighton.
Brighton v West Ham: talkSPORT coverage
This Premier League clash will take place on Sunday, May 22.
Kick-off at the Amex is set for 4pm.
Coverage will be live on the talkSPORT App and commentary from the south coast will come from Rich Wolfenden.
To tune in to talkSPORT or talkSPORT 2, click HERE for the live stream.
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Brighton v West Ham: Team news
The home side will have pretty much a full squad to choose from, with Jakub Moder the only player definitely out.
Because of a groin problem, Enock Mwepu has missed the last two games, but he is expected back on Sunday.
Meanwhile, the away side won't have Angelo Ogbonna or Issa Diop for the final match of the year.
But Said Benrahma should be in the squad after missing last week's draw with Manchester City.
Moyes also confirmed Mark Noble would be involved for what will be his final appearance as a Hammer.
Brighton v West Ham: What has been said?
West Ham boss David Moyes: "I think that we're going into the game having already got European football.
"It's a huge plus for us and a great achievement, but the thought we could finish sixth again, after the year we've had and the competitions… whatever we've done this year, we've been able to maintain this season, which is a good sign, and I hope we can roughly maintain and build on it for next season as well.
"This season we've had 12 extra matches and gone further in the Carabao Cup than we have for a long time - even in the FA Cup.
"All those things add up as extra games, and we've found it quite difficult, but we've also found it quite enjoyable. The European games were incredibly exciting.
"In some of the Cups, we have decent draws, but in the Carabao Cup we had a really tough draw."
Brighton v West Ham: Match stats
Brighton are unbeaten in all nine of their Premier League meetings with West Ham (W3 D6) - it's both the most they've faced an opponent without ever losing, and the most the Hammers have faced a side without ever winning in the competition.
West Ham have won just one of their last 10 away league games against Brighton (D3 L6), winning 1-0 in the Championship in October 2011 thanks to a Kevin Nolan goal.
Each of the last six Premier League meetings between Brighton and West Ham have been drawn; in English top-flight history only three fixtures have ever been drawn seven times in a row - Chelsea v West Bromwich Albion (1921-1924), Aston Villa v West Ham (1998-2001) and Birmingham v Liverpool (2005-2010).
Brighton have lost their final league game in three of their four Premier League campaigns, with the exception being a 2-1 win at Burnley in 2019-20.
West Ham have won their final Premier League game in four of the last five campaigns (D1), last losing against Stoke City in 2015-16.
After losing six consecutive league games in February and March, Brighton have lost just one of their last eight since (W4 D3). Each of the Seagulls' four victories in that run have come against teams in the top eight of the table.
Just 19 of Brighton's 48 Premier League points this season have come in home games (40%), with only Watford (35%) earning a lower share of their points at their own ground this term.
Brighton's Danny Welbeck has scored 11 goals in his two Premier League campaigns with Brighton (48 games), one more than he had in his previous four seasons with Arsenal/Watford (70 games). He's netted four Premier League goals against West Ham, only netting more in the competition against Aston Villa (5).
Jarrod Bowen is West Ham's highest Premier League goalscorer this season with 12 goals, the most by a Hammers player in a single campaign since Marlon Harewood in 2005-06 (14). However, just two of Bowen's 12 strikes this season have come away from home.
If he plays, this would be Mark Noble's 414th and final Premier League appearance for West Ham, the seventh most appearances for a single side in the competition's history. He has more assists in the Premier League than any other Hammer (35), while only Michail Antonio (55) has scored more goals for the club than Noble (47).