The Hammers currently sit five places above the relegation zone but are not completely safe from biting the dust with five matches to go.
Ayew, who scored in last weekend's draw with Swansea City, has been one of the club's best performers, having netted four times in his last eight league outings.
"Everton are a big team with big players and it’s a big game and we need to [win the] points. It’s important," Ayew told his club's official website.
"We saw the atmosphere in the last game against Swansea and we need the same again. We will give it our best.
"We need to prepare and hopefully the fans will be there in their numbers for Everton at home and hopefully we give them something to cheer as well."
Everton currently occupy the eighth position.
Ayew joined West Ham on a club record £20.5 million deal last summer.
Before transferring to the Hammers, he scored 12 goals in 34 league appearances to help Swansea finish 12th.