The midfielder is due to have a late fitness test ahead of the Premier League contest at the Emirates, while Kieran Gibbs was also rumoured to be a doubt for the match because of a hip injury.
However, Wenger has stated that Gibbs is likely to make the cut, while Wilshere could also be absent from Tuesday's Champions League tie against Anderlecht.
"I'm quite positive on Gibbs, I don't think Wilshere will be available," Wenger said in this morning's press conference. "It's a very short term with Wilshere. He got a kick on his knee. I don't know if he'll be fit for Tuesday. Certainly [against] Swansea [next Sunday]."