Barca are believed to have put a £5 million price tag on Song, but the Irons are hoping to persuade the Catalan club to let him leave on a free and take on his entire £70,000-a-week wages.
The Cameroon midfielder still two years remaining on his Barca contract and the La Liga champions are reluctant to pay a share of his current salary for that period if no club is willing to match it.
West Ham are one club who are happy to offer Song his full wages – on the condition that Barca to let him go for free or significantly drop the asking price.
27-year-old Song spent last season on loan at the Boleyn Ground, making 31 appearances in all competitions. He previously played for Arsenal in the Premier League.