The Cameroonian midfielder departed Arsenal to join the La LIga giants in 2012 in a £15m deal, but has struggled to impose himself at the Nou Camp.
Despite being able to play in a variety of roles in the centre of the pitch, Song has barely featured for Barca due to a number of disappointing displays and competition for places.
His former club are said to be interested in bringing him back to England, but they are likely to face competition from Manchester City and Manchester United.
The Catalans are aware that they will not recoup the fee they paid for the enforcer a couple of years ago, and are thought to be willing to take a significantly lower sum to get him off of their books.
Song used to be a regular in the Gunners’ starting XI, but he only managed 20 appearances in his debut season in Spain and even fewer this year under Tata Martino.
The 26-year-old himself has declared a desire to stay at Barca in the past, but an end of season move may appeal to him as he looks to get his career back on track.