The Gunners are widely expected to strengthen this month, having already started to free-up space in the squad by off-loading Marouane Chamakh and Johan Djourou. While Wenger has been linked with David Villa, Adrian Lopez, Lucas Biglia and Yann M'Vila, the Arsenal manager 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.
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."