The Cameroonian ace only left the Gunners last year to move to La Liga, but has struggled to establish himself at the Nou Camp.
The presence of Sergio Busquets has limited Song’s opportunities in his preferred role as the anchor of the midfield, while he has also been used to minimal effect at centre-back.
New boss Tata Martino is believed to be looking alter the Spaniards’ playing style, but he has already seen enough of the 26-year-old to sanction his sale.
Despite the club having spent £15m on Song a little over 12 months ago, they are ready to take a £5m hit on the midfielder to move him on this winter.
Both Arsenal and United are both believed to have been alerted by the development, and could launch offers for Song.
Emirates Stadium chief Arsene Wenger is known to be looking at securing a combative enforcer and may be ready to bring back his former charge, who was a consistent performer for the London club.
Meanwhile David Moyes is looking at Song as he looks to inject some dynamism into his rather pedestrian midfield set-up.