While Olivier Giroud has eight goals in all competitions this season, Theo Walcott has only recently recovered from an abdominal injury while Lukas Podolski remains out injured.
Despite their lack of bodies up front, Wenger is confident he has sufficient strength in depth to maintain the leaders' Premier League title challenge, although he did not rule out making acquisitions - provided the conditions are right.
"I think we can win the title without signing a striker," he said.
"Theo gives us qualities that other players haven’t got. It’s a different option. Theo also gives us an opportunity to (have) a mobile striker. If we lose Giroud today we have nobody with body weight up front.
"Podolski is not back but he shouldn't be too far now. They make it less critical to sign a striker."
Arsenal attempted to bring Luis Suarez to the club in the close season while there was also reported interest in the likes of Edin Dzeko and Karim Benzema.
Wenger feels there are issues involved with signing players in the January transfer window, and admits he has made errors in the market before.
"Look, I am not against it (a January signing). I don't say I never make a mistake - I certainly made some," he added.
"Sometimes it is because we didn’t sign the right player.
"It is always difficult in the middle of the season. If somebody is doing well somewhere the clubs do not necessarily want to sell him. They can wait until the end of the season. Most of the time it is because we didn't find (him)."
