The 20-year-old suffered a calf injury in the 3-1 victory over Fulham at Craven Cottage last weekend and was replaced at half-time.
Everton boss Roberto Martinez has confirmed club staff are monitoring the situation ahead of a match that could define the team's season.
If Everton beat the Gunners they would move one point behind their fourth place opponents with a game in hand.
And Martinez is hopeful the England international will be fit for the match as the team pursue a Champions League place for next season.
"He is such a powerful boy that he coped with that knock well but obviously it was a problem straight after when the body gets cold," Martinez said.
"He's such a quick healer and a young man so we hope he is going to recover in time for the game on Sunday.
"Over the next three or four days we will have a clearer idea of where he is and we are going to treat every day as it comes."
Everton are also taking a cautious approach with England defender Phil Jagielka, who has missed the last six matches with a hamstring problem.
"It's important that with the amount of games we will be experiencing that we look after Phil and make sure he is allowed to build a good degree of match fitness," Martinez added.