The 31-year-old has fallen down the pecking order at the Nou Camp and is keen on a move away, with the Premier League rumoured to be his preferred destination.
Reds boss Brendan Rodgers is keen to bolster his forward line in January to provide support for Luis Suarez, who is the club's only fit senior striker.
A deal for Chelsea forward Daniel Sturridge is close to being wrapped up and it appears Rodgers is ready to add Villa to his squad as well.
However, while the Reds would prefer a loan move for the former Valencia hit-man, Barcelona will only entertain a permanent deal.
They value the forward at around £16million, which may be out of Liverpool's price range, with Rodgers previously indicating he is not prepared to pay over the odds for players in January.