The England international hasn't played for the Gunners in over a year after suffering injury during pre-season in 2011.
The 20-year-old underwent a knee operation at the end of the last campaign and Wenger says that it won't be too much longer before Wilshere is back on the pitch.
"He is looking very good in training," said Wenger. "Close, it depends what you call close.
"I would still give him a month. But it looks very good. In a month he should be starting to play again.
"Look at our midfield; you have Arteta, Cazorla, Diaby, Wilshere, Coquelin, Rosicky, Ramsey. There is a fight for places and there is quality."