The Cameroon international has been linked with a move to Old Trafford after failing to secure a first team place at the Nou Camp. Italian giants AC Milan are also said to be interested.
Song is thought to be keen on a switch in order to play regular first team football, although Barcelona remain unsure as to whether they want to sell a player they signed for £16million barely a year ago.
Reports in Spain suggest the Catalan club will look to hold onto Song until the end of the season at least, meaning a January move to Old Trafford seems unlikely at this point.
It is also thought Song wants the opportunity to win over new coach Gerardo Martino before deciding on his future.
Barcelona will want to recoup the £16million they spent on Song if they are to sell him, with United understood to have made an offer in the summer that didn’t match their asking price.
David Moyes made no secret of his desire to recruit a midfielder in the summer, and saw bids for Song and his Barcelona and former Arsenal teammate Cesc Fabregas rejected.
Maraoune Fellaini became Moyes’s only big name summer signing on deadline day, although the Manchester United manager is set to try and strengthen further in January.