The ex-Gunner left Arsenal for Barcelona in the 2012 summer window, but has struggled to nail down a first-team place at the Nou Camp.
And the report claims the 26-year-old would consider a return to Arsenal at the earliest possible opportunity in January.
The Cameroonian has been restricted to just three league appearances so far this term, following on from a disappointing first campaign in Spain during which he failed to dislodge Sergio Busquets from the starting lineup.
He's been forced to operate at centre-back on occasion, and he's believed to be considering a transfer in the winter window to secure football in his preferred position.
Arsenal and Manchester United were both mentioned in the report as interested parties, with David Moyes in particular said to be plotting a move to strengthen his midfield.
United boast a financial advantage over their Premier League rivals, while the prospect of returning to Arsenal could favour the Gunners should it become a straight fight for his signature in January.
Song left Arsenal for Barca for a fee in the region of €19m, but the report fails to mention any buy-back clause in the Cameroonian's contract.