Miroslav Klose is frustrated by his lack of playing time at Lazio this season, but says he will not leave this winter.
Fernando Torres will join Milan permanently on January 5 ahead of his expected return to Atletico Madrid.
The Gunners are widely expected to strengthen this month, having already started to free-up space in the squad by off-loading Moroccan striker Marouane Chamakh on a six-month loan deal to West Ham and Swiss defender Johan Djourou to Hannover.
While Wenger has been linked with a string of reinforcements from Barcelona forward David Villa, Atletico Madrid frontman Adrian Lopez, Anderlecht's Argentina midfielder Lucas Biglia, Yann M'Vila from Rennes and even former captain Thierry Henry on loan again, the Arsenal manager maintains he will only be tempted should a player of the required quality become available.
"We are on the market and if we find the right players, we will do something", Wenger told Arsenal Player.
Wenger is said to be keen on Villa, who was a substitute for Barcelona's 4-0 win over Espanyol at the weekend as he continues his reintegration after a spell out with a broken leg.
However, club president Sandro Rosell insists the 31-year-old, signed in a £31million deal from Valencia in 2010, is going nowhere.
Speaking to Catalan radio station RAC1, Rosell said: "I completely rule out the transfer of Villa during the winter market.
"He is ours and we need him, there is a lot of the season left."
Elsewhere, Sao Paulo are confident they can make Denilson's loan move into a permanent transfer, although the departure of Andrey Arshavin appears unlikely as the Russian playmaker will be drafted into first-team contention again as cover for Gervinho, who is away at the African Nations Cup with Ivory Coast.
Wenger is also determined to sign up forward Theo Walcott to a new contract sooner rather than later, with suggestions a deal, reportedly worth close to £100,000-a-week, could even be announced ahead of Sunday's clash with Manchester City.
On the pitch, Arsenal now head into a crucial run of fixtures which may well define their season.
Following a dramatic 2-2 draw at Swansea in the FA Cup, the Gunners face a replay next week just a few days after the Barclays Premier League champions Manchester City come to Emirates Stadium.
Arsenal then travel to Chelsea on January 20, before tackling West Ham in their rearranged Boxing Day fixture which is followed by a possible FA Cup fourth-round tie at Brighton ahead of the visit of Liverpool, with a Champions League last-16 tie against Bayern Munich also on the horizon.
Wenger said: "We have shown character and quality (against Swansea) and those are good ingredients for the coming weeks."
Defender Per Mertesacker, meanwhile, feels the Gunners can meet their busy schedule head on.
He said: "We are in a good way but we have to keep our focus on these games [against Manchester City and Chelsea] and the knockout stages of the Champions League. We have to win those games now," the German centre-back said.
"We are always looking to win something and we can achieve something with this group. We have a lively group so our thoughts are now on the next match, that is the most important thing for us, not what's going to happen in May.
"We have a few targets in our team that are possible this year. We won't talk about it, we'll just see what happens in the next few important weeks on the pitch."