The two Premier League heavyweights are particularly interested in Song because he qualifies as a home-grown player even though he played for Cameroon.
Song, who spent last year on loan at West Ham United, has two years left on his Barcelona contract.
West Ham are still hopeful of turning their loan agreement into a permanent transfer but Sky sources understand there is interest from several other clubs – including Chelsea and City.
The 27-year-old, who spent six seasons with Arsenal before moving to Catalonia three years ago, made 28 Premier League appearances for the Hammers last season.
Barcelona, who paid £15m for the player, are believed to be looking for a fee of around £5m from any transfer. His contract at the Nou Camp is believed to be worth £70,000-per-week.