The Gunners midfielder has missed over a year of action after suffering a serious ankle injury, while numerous setbacks on his road to recovery have meant he missed the entire 2011-12 Premier League season and Euro 2012.
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Indeed, Wenger has previously stated that he would be taking a very cautious approach with the 20-year-old, but appears optimistic over a return.
"It looks very good for Wilshere," Wenger told reporters. "I would say give him a month."
Wenger was speaking after the Gunners' 2-0 victory over Liverpool at Anfield, in which Thomas Vermaelen also picked up a knock, but he also allayed fears over an injury, saying his defender should be fine.
He added: "Vermaelen just had a kick. I didn't see exactly what happened but I don't think it is too serious and he should be alright."
Wenger also commented on the return of Abou Diaby, who controlled the midfield as he continues his return to first team football following a torrid time with injuries in recent years, saying there is more to come from the Frenchman.
He continued: "It is massive for us to have Diaby back from injury too. He looks in good shape, and there is a lot more to come from him."