The former Arsenal man has been a peripheral figure at the Nou Camp for some time – making just 28 outings this season – and is believed to be available for the right price once the coming transfer window kicks into action.
This has alerted David Moyes, who has indicated to Barca that he is ready to pay £12.5m for the Cameroonian.
The La Liga champions are understood to be open to the sum on offer, with recouping most of the £15m paid two years ago attractive to them.
As it stands, Barcelona are to be banned for the coming two windows after breaching FIFA transfer rules, which will prevent them from either buying or selling payers.
Yet it is believed that they will appeal to allow them to conduct some business in the coming months.
Liverpool have also been linked with Song, but United are understood to be firmly in the driving seat with Moyes desperate to add to his struggling midfield.
The 26-year-old can also provide cover at centre-back, which is said to be a tempting factor for the Red Devils chief as he plans for life without Nemanja Vidic and the possible exit of Rio Ferdinand.
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