There have been suggestions that the Gunners are keen on bringing the 31-year-old Spain international to the Emirates before the close of the transfer window as they look to increase their firepower.
However, these rumours have been dismissed by the London club and Barcelona also reportedly have no intention of selling the player at this time.
Villa played the full 90 minutes in Barcelona's 5-1 win over Osasuna on Sunday but has failed to win a regular starting spot this term after missing last season with a broken leg.
He has made 85 appearances for Spain and is the country's all-time leading goalscorer with 53 goals.
Arsenal were also linked with Villa earlier this month when Barcelona president Sandro Rosell insisted the striker would not be leaving the club.
"I completely rule out the transfer of Villa during the winter market," Rossell said. "He is ours and we need him, there is a lot of the season left."