The Reds are understood to have submitted a bid for the former Arsenal man, whom is free to leave the Catalans for the right price after a disappointing two-year stint at the Camp Nou.
Although the details are unknown, reports suggest that a fee of around £8m is likely to be enough to bag the Cameroonian.
Liverpool have been very active in the transfer market already this summer, but Brendan Rodgers has talked up a need for yet more signing over the course of the past few days.
Song would be a player to fill a number of roles, with the 26-year-old able to fill in at centre-back as well as in a host of midfield positions.
Manchester United have also been linked with the African ace, but their interest is rumoured to have cooled with Arturo Vidal their prime target.
Galatasaray are thought to have made a bid as well, but a return to the Premier League is liable to more tempting for the player.