The Wales international, who has scored eight Premier League goals this season, has not featured since limping out of the Boxing Day clash with West Ham at Upton Park.
However, manager Arsene Wenger has confirmed the 23-year-old may make his comeback at Goodison Park in what could prove a crucial game in deciding the final UEFA Champions League place.
"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. (Abou) Diaby is back on the pitches, so that is good news."
Arsenal have a lengthy injury list currently, with the likes of Mesut Ozil, Jack Wilshere and Theo Walcott all ruled out for various lengths of time.
The latter is not expected to play again this season and Wilshere is also some way off a recovery, although Ozil could return after next week's FA Cup semi-final with Wigan Athletic.
"At the moment that is all because the other injured players are not back, not Wilshere, not Ozil. Everybody else is alright," Wenger added.
"The FA Cup will be too soon for (Ozil), but he will hopefully be back soon after that."
