The Belgium player has never really fitted in at Stamford Bridge, but has had impressive loan spells at both West Brom and Everton.
Last season Lukaku netted 17 times for West Brom and this season has netted five for Everton in just eight starts.
Now Manchester City, with one eye on the possible departure of Edin Dzeko, are said to have made an enquiry.
However, they may face competition as the 20 year-old has also caught the eye of Arsenal.