The 20-year-old was taken off with a calf problem during the half-time interval of Everton's 3-1 win over Fulham last Sunday.
"Ross had a knock on his calf and he is recovering well from it," Martinez told Everton TV. "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.
"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."
If Everton win this weekend, they will be one point behind fourth-placed Arsenal in the Premier League table with a game in hand.