The Gunners must decide whether to risk the midfielder at the Emirates, or rest him ahead of a crucial UEFA Champions League clash with Bayern Munich on Tuesday.
Wilshere was forced off during a 1-0 win over Sunderland last weekend, just days after completing 90 minutes for England in a friendly date with Brazil.
Wenger has already warned of burnout when it comes to his talented 21-year-old and may err on the side of caution when it comes to his involvement in FA Cup competition.
"Jack is looking better, but is still a doubt. He got a kick on the thigh," he said.
Meanwhile, Thomas Vermaelen has revealed that he is making positive progress in his recovery from an ankle problem.
The Belgian defender has been forced to sit out Arsenal's last two fixtures after picking up a knock, but expects to come back into contention in the not too distant future.
Vermalen told Arsenal's official Twitter account during a Q&A session with fans: "At the moment I feel great, I trained all week, so hopefully I will be back really quickly."