Wenger has seen his defence frequently criticised this season despite signing Per Mertesacker, but despite question-marks about the performances of players like Sebastien Squillaci and Johan Djourou, the Frenchman has ruled out any moves for a central defender in January.
Alex has been told he can leave Stamford Bridge in the winter window, and Tottenham manager Harry Redknapp has already declared his interest in the Brazilian. But Wenger was quick to quash any speculation linking Arsenal with a bid.
"We will not be on the market for any centre-back, I can assure you,” Wenger said on SkySports.
Wenger signed German international Mertesacker and Brazilian Andre Santos in the summer to boost his defensive options, but injuries to Kieran Gibbs, Bacary Sagna, Carl Jenkinson and now Santos have left the club exposed in the full-back positions - something former Werder Bremen centre-back Mertesacker would like to see addressed in January.
"We need more full-backs I think! It's not good for the squad if so many full-backs are injured, but what can I say?
"We have to manage the situation. We have had some bad situations with injuries in the last month but we managed quite well.
"We are looking forward to climbing the league more and more. We have had a lot of pressure to get to fifth in the last month but we need more consistency, in December more than ever.
"Therefore I hope we can pick up a lot of points to get to the top four. We want more than that, of course."
The Gunners' full-back problems have seen centre-back Laurent Koscielny fill in at right-back, while another centre-half, Thomas Vermaelen, looks set to cover at left-back until Gibbs or Santos is fit to return.