Per the source, the Hammers have made City an enquiry regarding loaning the Ivory Coast international this season.
Bony has called out of favour with City boss Pep Guardiola and has been left out of the match-day squad for all three of the Citizens competitive games this season.
The Hammers are desperate for a striker following injuries to summer signing Andrew Ayew as well as England international Andy Carroll.
West Ham boss Slaven Bilic could face competition from his former club Besiktas who are currently in talks with the Citizens over the loan transfer of Bony a source close to the Istanbul giants told Turkish-football.com.
Skybet slashed the Istanbul giants odds to sign the powerful striker from 19 to 4 as a result of negotiations reaching an advanced stage.
Bony is a proven Premier League striker having scored 26 goals in 54 games for Swansea City before his move to City which did not pan out as expected.
The powerful striker found the back of the net just six times in 36 games for City since joining.