Ramsey has not featured since suffering a thigh strain at West Ham on Boxing Day, robbing Wenger of one of his key performers with the 23-year-old having scored an impressive 13 goals in the opening part of the season.
Having initially expected only a six-week absence, Ramsey suffered a couple of niggling setbacks, but is now in line to make the trip to Merseyside as Arsenal look to take a grip on fourth place ahead of their FA Cup semi-final at Wembley on April 7.
"Aaron and Nacho Monreal are back training with 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, www.arsenal.com on Thursday.
Midfielder Diaby has not featured for more than a year because of a serious knee injury - the latest in a long-line of setbacks for the combative France international, and could provide a surprise welcome boost for the closing few fixtures, with England international Jack Wilshere also facing a race against time to be fit for the run-in.
Centre-back Laurent Koscielny may be available for the trip to Wembley against Sky Bet Championship side Wigan next weekend following his calf problem.
Wenger, though, confirmed there would be no swift return for German playmaker Mesut Ozil, who has been out since suffering a hamstring injury in the Champions League exit at Bayern Munich last month.
"The FA Cup will be too soon for him, but he will hopefully be back soon after that," said the Gunners boss.
The jury is still out for many on Ozil, who has shown just glimpses of his talents since arriving in a much-heralded club-record £42.5million transfer on deadline day of the summer window.
However, former Gunners goalkeeper Jens Lehmann has no doubts his compatriot can go on to great things at the Emirates Stadium.
"Mesut Ozil will be a big success at Arsenal," Lehmann told talkSPORT.
"You have to remember that every player who has come from abroad needs to get used to the rhythm of the Premier League.
"You don't know how your body is going to react after the winter period - in no other league is it so hard to play throughout the whole season. You get a little break in Spain and Germany.
"It is his first season at Arsenal, but he is a fantastic player."
Elsewhere, Swiss defender Johan Djourou looks set to make his loan move to Bundesliga side Hamburg permanent in the summer.