The former Valencia striker has been linked with a move away from the Nou Camp after finding himself down the pecking order in manager Tito Vilanova's thoughts.
The 31-year-old is believed to be keen on a move to the Premier League and reports this week suggested that Tottenham had moved to secure his services when the summer transfer window opens.
According to Sport, Liverpool and Arsenal - who were linked with a move for Villa in Janaury - are also in the running for the forward's signature.
Arsenal appear keen on landing a forward this summer and have been credited with an interest in Fiorentina's Stevan Jovetic, while Gunners boss Arsene Wenger has revealed he is close to landing French youngster Yaya Sanogo.
Sport claim Arsenal are in the driving seat to land Villa because they can offer him Champions League football.
Liverpool may decide to step up their pursuit of the Spanish record scorer after the revelation that Luis Suarez wants to leave Anfield this summer.
The Uruguayan has confirmed in a a series of interviews this week that he is unhappy with life in England and is angling for a move away from Merseyside.
Liverpool could also face losing Pepe Reina, who is a target for Barcelona.