The 23-year-old Wales international has not featured for the Gunners since suffering a thigh strain during the 3-1 win at West Ham on Boxing Day.
Ramsey, who scored 13 goals in the first half of the season, was only expected to be sidelined for around six weeks but a couple of niggling setbacks have delayed his return.
However, he is now in line to make a welcome comeback as Arsenal take on the Toffees in a match which will have a crucial bearing on whether or not they can secure a top-four finish.
Spanish left-back Nacho Monreal could also feature at Goodison Park, while midfielder Abou Diaby is closing in on a return after being out for more than a year with a serious knee injury.
"Aaron and Nacho Monreal are back training with the squad, so that is good news. Hopefully they will be available for Sunday. Diaby is back on the pitches, so that is good news," said Wenger.
Midfielders Jack Wilshere and Mesut Ozil remain on the sidelines but centre-back Laurent Koscielny may be available for the FA Cup semi-final against Wigan next weekend following his calf problem.
"The FA Cup will be too soon for Ozil, but he will hopefully be back soon after that," added Wenger.
Ozil later wrote on his Facebook page about a determination to return in good form, but at the right time.
The German said: "Dear fans, I can assure you that I'm doing my best to return to the pitch as soon as possible. But in the end, only two things matter: to have confidence in yourself and to be patient!"
Watch Everton take on Arsenal live on Sky Sports 1HD on Sunday at 1.30pm.