The Wales international picked up an untimely injury on the back of netting a hat-trick in the 5-1 win against Everton on February 3, missing his side's last three matches since then.
Ramsey is expected to undergo further tests on his groin injury at some point on Friday, before a decision is made at the weekend as to whether to include the 27-year-old in the 18-man squad to face Man City.
"We'll see how his evolution goes now from today until Sunday," Wenger told reporters at his pre-match press conference. "I don't rule him out yet, it depends on how well he can improve with the intensity of training until Sunday."
Fellow midfielder Mesut Ozil is also a minor doubt, having been struck down by illness once again in recent days to rule him out of the Europa League tie against Ostersunds on Thursday night.
Wenger is hopeful of having the German playmaker in his ranks, however, telling reporters: "I saw Ozil this morning. He had a good session yesterday that he absorbed well so we have to see how he responds to it today but I think he will be alright.
"You want all of your best players available and of course he is an important player for us."
Henrikh Mkhitaryan will definitely miss out for Arsenal due to his previous participation in the competition with Manchester United, while Alexandre Lacazette is injured and Santi Cazorla is a long-term absentee.