Song would prove to be a useful signing for both clubs as he qualifies as a home-grown player.
Man City are still in need of 2 more home-grown players for this season, and Song would fulfil one of them spots.
The midfielder was on loan at West Ham for the duration of last season, but does still have two years left on his contract at Barcelona.
As well as the other two, Bilic’s side are also hopeful of turning the loan in to a permanent move but it is thought Song is being tracked by a number of other clubs, including Chelsea and City.
The 27-year-old spent six years with Arsenal, which is where he gets his home-grown status from, before moving out to Spain with Barcelona.
The Catalan Giants paid £15m and gave Song a contract worth £70,000 but are now thought to be looking at a fee in the region of £5m.