The Belgium international is currently on loan at Everton, but despite impressing on Merseyside he is understood to be available for around £20m-£25m at the end of the season.
Jose Mourinho is said to be unconvinced by the 20-year-old, which has alerted a host of clubs – including Tottenham and the Toffees.
Now City have joined the hunt, with Manuel Pellegrini plotting for the possible sale of Edin Dzeko.
The Bosnian ace looks likely to leave the Etihad Stadium after a disappointing spell at the club, and Sky Blues’ chief is desperate to land a replacement for him.
Lukaku is seen as the ideal option, with the youngster possessing, arguably, better physical attributes than Dzeko.
Chelsea are unlikely to be keen to do business with a direct rival, but with the Manchester club able to pay in full and up front, Mourinho may be tempted as he plans his own moves for a top class striker.
Lukaku himself is probable to be open to the move, with City virtually guaranteed to be able to offer Champions League football.
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