The Vitesse Arnhem forward has been attracting the attention of a number of top Premier League and European sides following a string of impressive displays in the Eredivisie.
An excellent 20 goals in 36 appearances last term attracted the attention of Newcastle over the summer, but a transfer never came to fruition.
Now the Blues are believed to be interested in the 23-year-old, who would be keen to play in England.
Roberto Di Matteo is woefully short on central striking options, with Spaniard Fernando Torres failing to impress since his £50m arrival in 2011 and back-up hit-man Daniel Sturridge rumoured to be unhappy at the club.
Reports suggest that Bony could be available for around £8m in January, with his employers likely to be interested in cashing in while his stock remains high.
Serie A duo Napoli and Udinese are also keen and would rival any bid made by the Londoners.
The front-man began his career with Ivorian club Issia Wazi, before he was snapped up as a youngster by Sparta Prague.
After averaging a goal every three games between 2008 and 2011, Vitesse came calling taking Bony to Holland where he has continued to impress.