While Wenger is confident his squad does have the needed strength in depth to finally last the distance in the title race, the Arsenal manager maintains anyone who is brought in will have to be the right calibre of player - with Atletico Madrid frontman Diego Costa one reported January target.
"We are like many clubs, certainly (we are) on alert," Wenger said.
"If something special turns up we will not turn it down, but we are not as well desperate because we have a big depth in our squad.
"We have shown that because our midfield at West Ham and at Newcastle was completely different, we changed three players and we still managed to have a very strong team."
Wenger continued: "I am quite confident with our squad.
"As has been mentioned, maybe up front we are a bit shorter with specialised people because most of the big clubs have three specialised central strikers, we have only two because (Yaya) Sanogo is not ready yet, so maybe if that something special opportunity turns up, we will not turn it down, but everywhere else we are in no need at all (to buy)."
Giroud's second-half header secured victory at Newcastle to end his mini-goal drought.
The 27-year-old France international revealed he would "rather not see a new striker come in" during the January window.
Wenger, though, maintains Arsenal are not looking to exchange their 11-goal forward, rather offer him support.
"Would you expect anything different from a striker?" said Wenger when asked what he thought of Giroud's comments to French TV.
"I believe we have to give him credit for one thing, that physically he has coped with it until now in a remarkable way and with a fantastic combative attitude.
"I don't know if we will do something or not (in January), but it is not to replace Olivier Giroud - we have a great confidence in Olivier Giroud."
Arsenal hope Giroud's lay-off will not prove significant, with the forward having already targetted a return against Tottenham in the FA Cup third-round clash this weekend.
Source : PA
Source: PA