Villa has allegedly become unsettled at the Nou Camp after the club hesitated on offering him a new contract following the signing of Alexis Sanchez in the summer.
Radio station, Cedena Ser claims that Liverpool and also Chelsea have been in contact with Barca regarding the price and availability of Spain's record goalscorer.
The 29 year old is also said to be unhappy at Pep Guardiola's preference to play him on the wing to accommodate Lionel Messi.