The Spain international has been heavily linked with a move to the north London outfit this month after a frustrating spell at the La Liga leaders.
The 31-year-old has scored five goals this season, but the World Cup winner has only started seven La Liga games, with the former Valencia man out-of-favour under Tito Vilanova.
The Gunners were keen on Villa, but Wenger revealed Barcelona are unwilling to sell the striker.
“Barcelona don’t want to sell, they’ve made that clear. I said they don’t want to sell, I didn’t say he was target,” said Wenger.
Meanwhile, Beckham has been training with the Gunners after leaving MLS outfit LA Galaxy in November, prompting reports the 37-year-old could join Wenger’s side.
However, the Arsenal manager was adamant the former Three Lions skipper is only training with the club to improve his fitness.
“He has asked to come here and to work on his fitness. He has not done anything for a long, long time,” added Wenger.
“It’s purely for fitness. There’s no speculation about signing or anything.”
Earlier in January, Marouane Chamakh and Johan Djourou both left on loan deals until the end of the season, and Wenger insisted the Gunners were still looking to strengthen before Thursday’s deadline.
“We are still trying, but it’s hard to sign players in January who can improve you.”