Arsene Wenger insisted earlier this week that his interest in Villa was 'dead', but the report claims the Arsenal boss has submitted an offer, thought to be worth between £10-£11m, for the Spain international.
The 31-year-old striker has struggled to establish himself as a first-team regular since returning from injury, and speculation has linked him with a move to the Premier League.
Villa spent eight months on the sidelines with a broken leg, but made his comeback this season.
Despite scoring a number of crucial goals, the former-Valencia star has found it difficult to cement a regular starting spot at the Nou Camp under Tito Vilanova.
He was an unused substitute again last night as Barcelona drew 1-1 against Real Madrid in the Copa Del Rey semi-final first-leg. His 90 minutes in the 5-1 defeat of Osasuna last weekend was his first full match for the club since November 2011.
And the report suggests Arsenal are hoping to capitalise by offering him first-team football in England. The Gunners are set to make one final push to land the forward, with Goal.com's Spanish sources claiming Villa is 'very keen' to join Arsenal.
Wenger's approach for Spain's all-time record goalscorer was reportedly turned down earlier this month, but the Gunners boss has refused to accept defeat.
The report suggests he's willing to pay up to £13.8m to bring the striker to the Emirates Stadium, while the north London club are prepared to offer him £110,000-a-week.
Negotiations between the clubs have centred on the structure of a potential deal, with Barcelona thought to owe Arsenal money due to scheduled payments for Cesc Fabregas and Alex Song.