The two clubs are battling for fourth place and a spot in next season's Champions League, with Arsenal one place and four points ahead of the Merseysiders, who have one game in hand.
"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 told the club website on Wednesday.
"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."
Barkley, capped three times by England, has been a driving force for the team this season, but Martinez will be wary of rushing him back if he is not fit, having said in February that he brought him back too early after suffering a broken toe.
The club was 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.
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