Goal.com exclusively revealed that the Gunners had abandoned their pursuit for Spain's all-time leading scorer, and are focusing on Atletico Madrid attacker Adrian instead. Whether that move is completed remains to be seen, however.
Speculation had linked the north London club with a bid for 31-year-old Villa, but the French coach has confirmed that he is not an option for the Premier League side.
The manager also ruled out stated that his club had not been in contact with West Ham about their midfielder Mohamed Diame, who has a clause in his contract allowing him to leave the club, rumoured to be around £3.5 million.
Wenger also stated that in general, deals in the January transfer window tend to be much bigger gambles than in the summer, and believes that there should be a limit to how many players clubs can bring in midway through the season.
"We have been linked with David Villa but nothing concrete there. We are not on the case," Wenger told reporters when asked about a potential move for the striker.
"We have not contacted West Ham about Diame.
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"The gamble is much bigger than during the summer. The number of players you are allowed to sign should be limited."
After ruling out the signing of Villa, Wenger went on to praise his current strikers Theo Walcott and Olivier Giroud, stating that the Englishman is improving and the Frenchman is developing his game in the Premier League, and also had kind words for Aaron Ramsey following the 5-1 win over West Ham.
"[Walcott] has improved everywhere. His finishing has improved a lot. [Giroud] is developing well and fights for the team," he added.
"[Ramsey] has a good performance [against West Ham] in a position that I think is made for him. We have to make up some ground. What was important for me was the manner we responded."