The Wales international has suffered a number of setbacks since picking up a thigh injury on Boxing Day.
However, after returning to full training, the 23-year-old could mark his comeback at Goodison Park alongside left-back Nacho Monreal.
"Aaron and Nacho Monreal are back training with the squad, so that is good news," Wenger told the club's official website. "Hopefully they will be available for Sunday."
The Gunners' hopes of finishing in the top four of the league table could suffer a blow should Everton win on Sunday, as the Merseyside outfit are currently four points behind Arsenal with a game in hand.