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."
