Arsenal have been linked to Spain’s record goal-scorer throughout January, but it has always been believed that they faced an uphill task to convince Barcelona to sanction a sale in midseason -- despite Villa’s limited appearances this campaign.
On Monday, Goal.com reported that an Arsenal representative was in Barcelona to try and secure a deal. According to the story, Arsenal were prepared to pay a fee of £13.8 million and match the 31-year-old’s wages of £110,000 a week.
But Wenger will now have to look elsewhere to strengthen his front line.
“Barcelona do not want to sell David Villa,” Wenger said, according to ESPN. “They've have made that very clear.
"You respect the desire that if someone says a player is not for transfer, you expect the other clubs not to try and buy him.
"In January it is very difficult to find a player who can strengthen a team like ours."
Wenger then said that there was “no” room for negotiation with Barcelona.
Arsenal could yet make a move for West Ham’s Mohamed Diame. Unlike Villa, the situation with Diame is fairly simple, with the Senegalese midfielder having a £3.5 million release clause in his contract. Wenger has claimed that he has not yet made a bid, but West Ham manager Sam Allardyce has admitted that he doesn't know what will happen.
"My understanding is that it's total confusion," he said, according to Sky Sports. "I'm as confused as anyone by what's happening.
"I sat there listening to what's going on but, deep down inside, behind the scenes, I speak to the chairman and, where we are at the moment, we're relatively comfortable regarding Mo Diame."
Allardyce also conceded that Diame’s recent assertions that he wanted to stay at West Ham will likely count for nothing if an offer from a big club arrives.
"Whatever he says to me today might change in an hour's time,” he added. “Whatever he says now, if Manchester United ring up in one hour's time, he's not going to want to stay, is he?
"So it doesn't matter what he's saying now. It could change between now and 11 o'clock Thursday night in the flick of a text, or an email, or a phone call.
"There are certain situations where, yes, we might lose the player. I hope we don't. But if the situation develops accordingly, there's going to be the chance we lose him. We're trying to keep him."
One midfielder who Arsenal claim they definitely won’t be signing is David Beckham -- that despite the former Manchester United star having begun training with the Gunners on Tuesday.
Beckham, 37, has been without a club since leaving the LA Galaxy late last year. But while he has been linked with a possible return to the Premier League, Wenger has said that it will not be with Arsenal.
“He has asked to come here and work on his fitness,” he explained. “He has not done anything for a long, long time. He comes here to try to get fit again.“There’s no speculation about signing or anything. He’s come here purely for fitness purposes.“We are open for people who behave well when they come here and who have made a great service for English football—you always try to help.”
Arsenal are said to maintain an interest in Torino center-back Angelo Ogbonna. The Daily Mirror reports that the Italy international is being chased by Manchester United, but Wenger and Everton’s David Moyes are also keen on the 24-year-old.
With Arsenal having allowed Johan Djourou to leave on-loan this month and their defense looking far from secure in recent times, a move for a defender cannot be ruled out.