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The sixth-place Hammers need just one point against Southampton on the final day of the season to secure Europa League football for next season.
A nine-goal swing would be needed on Sunday to deny West Ham any involvement in Europe in 2021-22, with seventh place bringing a spot in the inaugural Europa Conference League.
10,000 supporters will return to the London Stadium this weekend and Moyes has challenged his players to finish the job.
"It would be great if we could but we've got a game we can overcome, we have to try and win it," he said.
"That is the aim, we want to finish on a high. We've got ourselves in pole position, we've got to win."
Those who return to the London Stadium on Sunday will be seeing a different side to the one they last watched up close.
Moyes said: "It is great [having fans back], especially with the situation we are in and bringing them back to a real positive team who have played well and who have put in some brilliant performances and effort throughout the season."