The Blues are on the hunt for a new striker and Borussia Dortmund starlet Erling Harland has been their top target with a €175m fee mooted, but they are yet to make any concrete moves for him.
Chelsea have been keeping tabs on alternative targets to Haaland, including their former striker Lukaku, who is claimed to have rejected an offer worth €10m to return to Stamford Bridge.
The London side are keen to have Lukaku in their ranks and it has been claimed supremo Roman Abramovich has sent his son to Milan in a bid to persuade the Belgian to leave Inter.
However, according to Italian daily Gazzetta dello Sport, Lukaku has four main reasons to remain at Inter and is set to reject an improved offer from Chelsea, which is tipped to be worth €15m.
Firstly the hitman struggled to settle into life at Chelsea during his stint there, only making 15 appearances in Blues colours, spending two loan spells away and is not keen on a return to a club where he did find success.
In addition to that Lukaku loves plying his trade in Italy and is also enjoying life in Milan.
The striker has also found his rhythm at the San Siro and is grateful to Inter for giving him an opportunity to play with him sharing a good rapport with the Nerazzurri faithful.
Having led the Inter attack last term en route to the Serie A title, Lukaku also has his eyes set on repeating his heroics in the upcoming campaign under a new coach in Simone Inzaghi, which is also another main reason why he is not planning on leaving the club despite Chelsea being keen on him.