The midfielder has not featured for the Gunners since Boxing Day because of a thigh problem, while Nacho Monreal could also return for the fixture at Goodison Park.
Abou Diaby has also resumed full training having been sidelined for more than a year after suffering an anterior cruciate ligament injury.
"Aaron [Ramsey] and Nacho Monreal are back in the squad, so that is good news. Hopefully they will be available for Sunday. [Abou] Diaby is back on the pitches, so that is good news," Wenger told the club's official website.
Wenger also ruled Laurent Koscielny out of the match against Everton but confirmed the defender is in contention for the club's FA Cup semifinal against Wigan Athletic at Wembley on April 12.
"He is still out," said Wenger. "The earliest [he will be back] is next week, the latest is the week after."
Meanwhile, Mesut Ozil will miss the FA Cup tie against Wigan but Wenger said the German is likely to return from his hamstring injury toward the end of the month.
Fourth-place Arsenal heads into Sunday's clash with Everton four points ahead its opponent, but Roberto Martinez's side has a game in hand over the Gunners.