Ramsey limped off in injury-time of Wales' 2-1 Euro 2016 qualifying win in Andorra on Tuesday due to an ankle problem.
It was thought the 23-year-old - who missed around four months of last season with a thigh complaint - would likely miss Arsenal's home game with the Premier League champions this weekend.
However, Wenger revealed on Friday that Ramsey could figure against City.
"We [will] assess Ramsey today," he said. "He has a little chance to be available for Saturday. He has a minor ankle problem.
"I'm relieved that Ramsey's injury is not serious because we had a nightmare with him last year."
Wenger also confirmed that trio Kieran Gibbs, Mikel Arteta and Mesut Ozil are fit and will be in the squad, while transfer-deadline day signing Danny Welbeck is in contention for his debut.
Welbeck heads into encounter buoyed by his double in England's 2-0 victory over Switzerland on Monday and Wenger believes the former Manchester United forward will be a valuable asset to the squad.
"Danny Welbeck is young and I feel he can improve his career here," he added. "He is quick and is a great finisher. His best position is through the middle. He is happy and confident.
"I cannot tell you if he'll start [against City] but it's a possibility. I have to assess the squad.
"When you analyse Welbeck's game, he has the qualities to play down the middle but he is very versatile."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.