Rumours in Spain indicate that the ex-Arsenal man is surplus to requirements at the Nou Camp after struggling since his 2012 move to the club from the Emirates Stadium.
United have long been touted as favourites to bring him back to England, despite talk of Arsene Wenger being open to setting up a reunion with the Cameroonian.
However, Liverpool are now in the running for Song.
Brendan Rodgers is known to be looking at bolstering his squad during the off-season, with the Reds’ impressive campaign looking likely to present them with Champions League football for next term.
A holding midfielder to support Steven Gerrard and the injury-prone Lucas is seen as desirable, and the Barca man fits the bill.
Song is also able to cover at centre-back, and has long been complimented for his combative edge and passing vision.
The 26-year-old’s cousin Rigobert used to play at Anfield, which could tempt the enforcer to follow in his footsteps.
Although he is no longer wanted by the Catalans, Song is still valued at around £10m-£15m.