Arsenal had been linked with a move for their former player, but the report claims the Milan duo are now set to go head-to-head for his signature in January.
And in any case, Arsene Wenger re-signed another former-Gunner, Mathieu Flamini, in the summer to provide greater competition for the Arsenal midfield.
Song is under contract at the Nou Camp until the summer of 2017, but he's struggled to make an impression on the Barcelona first-team since his move from Arsenal in 2012.
A brief experiment at centre-back has not been the same success as Javier Mascherano's conversion, and Song is now tipped to leave the club, either this winter or next summer.
The report claims Inter Milan and AC Milan have sounded out Barcelona's interest in selling the 26-year-old midfielder.
And Arsenal are unlikely to rival the Italian pair for Song, despite the reported interest in the Cameroonian international.