The absence of Ivory Coast players Kolo Toure and Emmanuel Eboue could be a severe blow for the Gunners as the current Premier League leaders seek their first title since 2004.
But Wenger admits he may have to "suffer" during January rather than buy players who will end up being surplus to requirements.
"Kolo Toure goes off to the African Nations Cup shortly and we may lose Alex Song for it as well," said the Frenchman.
"Even with Johan Djourou returning from Birmingham we would then be left with three specialist centre-backs.
"If I signed another one we'd have too many after the African Nations. Sometimes you just have to suffer during the tournament and let your players play."