With Theo Walcott returning from injury and Lukas Podolski close to a recovery, the Gunners boss is reluctant to spend in a potentially difficult January transfer window
The Gunners are top of the table ahead of the visit of Southampton on Saturday, two points ahead of Liverpool thanks in no small part to the goals of Olivier Giroud, while Aaron Ramsey has contributed from midfield.
With Nicklas Bendtner likely to leave the club in January, Giroud could become Arsenal's only recognised central striker, but Wenger is confident the returning Theo Walcott and Lukas Podolski will ease the burden on the France international.
"Theo gives us qualities that other players haven’t got," he told reporters. "It’s a different option. Theo also gives us an opportunity to be a mobile striker. If we lose Giroud today, we have nobody with body weight up front.
"I think we can win the title without signing a striker. Podolski is not back but he shouldn’t be too far now. They make it less critical to sign a striker.
"Look, I am not against it [signing a player in January]. I don’t say I never make a mistake - I certainly made some. 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 [the right available player]."
Arsenal's meeting with third-placed Southampton is scheduled to get under way at 16:00CET.