The Spain international has been a reported target for the North London club and it had emerged that Arsenal had begun negotiations with the forward.
Despite these reports, Wenger has insisted that the Spanish giants are unwilling to offload the 31-year-old.
"Barcelona doesn't want to sell David Villa, they have made it very very clear," Wenger said in a press conference. "You respect the desire, if I say that somebody is not for transfer, I expect other clubs not to buy them."
Meanwhile, the Frenchman has confirmed that free agent David Beckham is training with the Gunners.