Villa is understood to be keen to secure a move away from the La Liga leaders after finding his first-team opportunities limited under new coach Tito Vilanova.
Barcelona president Sandro Rosell earlier this month insisted that Villa would not be leaving Camp Nou in the current transfer window – but the Gunners are still considering a bid as Arsène Wenger attempts to bolster his strike-force before 1 February.
The speculation comes after Barcelona coach Vilanova last week moved to end talk of a possible exit for the 31-year-old by insisting he still has an important role to play for his side this season.
“David will not leave, we are very happy with him,” Vilanova said. “It’s been a long recovery process [from his broken leg suffered in 2011], but we know his importance to the team, and we’re sure that he will help us.”
Villa, who joined Barça from Valencia for £31m in 2010, has scored 40 goals in 97 appearances in all competitions for the Catalan outfit.