The People says the Gunners are one of five clubs to have inquired about his availability but manager Wenger has opted for the personal touch to improve his chances of landing the 31-year-old Spain attacker.
Villa, who has scored 53 goals in 85 matches for Spain, is now hugely tempted by the possibility of a January move to the Emirates.
And while Barca are happy for discussions to take place, they have made it clear to both the player and Arsenal that they do not want to sell him until the summer.
Wenger is understood to have contacted Villa, with Barcelona’s permission, to explain his plans for the future. A deal this month would be worth £16million to the Catalan club – but that would drop to around £12m by the summer. Ideally Wenger wants him on board now but he is willing to wait until the summer if it is the only option.