Pep Guardiola's side are starting to put together their transfer plans for the summer and signing a new No.9 could be at the top of their list of priorities.
Sergio Aguero's current deal is due to expire at the end of the current campaign and no talks have taken place about a renewal.
Aguero has endured a nightmare campaign with injuries and COVID-19 and any new deal from City will depend on his fitness.
The Argentina international will not be short of suitors should he leave City with Paris Saint-Germain and Barcelona reportedly keen.
Aguero's departure will almost certainly force City into the market for one new striker with doubts over Gabriel Jesus' ability as a first-choice option.
Erling Haaland and Kylian Mbappe are obvious names for City to pursue but both are unlikely for different reasons.
Guardiola and City do not have a good relationship with Haaland's agent, Mino Raiola, and PSG are currently working on giving Mbappe a new long-term deal.
Harry Kane is admired by City but the Premier League leaders accept it will be almost impossible to prise him away from rivals Tottenham.
Signing Lukaku from Inter is far from straightforward but City deem it a cost-efficient option from all of their targets.
Lukaku's previous playing stint at United is not expected to be a problem if City step up their interest in the Belgium international.
The 27-year-old spent two years at Old Trafford before signing for Inter in the summer of 2019 and since then only Ciro Immobile (50) and Cristiano Ronaldo (47) have scored more Serie A goals (Lukaku - 37).
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