However, Chelsea are dissatisfied with the sum of cash that the Serie A side have offered for Lukaku, who has two years left on his deal at Stamford Bridge.
Napoli have reportedly offered £25.6million for Lukaku, but Chelsea are demanding closer to £40m.
Lukaku has spent the last two seasons on loan at Inter Milan and Roma, scoring 35 goals in that time, and wanrts to be reunited with Antonio Conte in Naples.
And Giovanni Manna, Napoli's sporting director, has been conducting talks in London to try and see a deal over the line, as per The Times.
Napoli are reportedly offering Victor Osimhen to Chelsea in a swap deal for Romelu Lukaku
Osimhen has been prolific in Serie A for multiple years and in 2022-23 dispatched 31 goals in all competitions, helping to fire Napoli to the title.
Despite a quieter 2023-24 season he is still hot property and much admired by Paris Saint-Germain as well as Saudi Arabian clubs.
So desired is Osimhen that two Chelsea icons are reaching out to him with persuasive intent: John Obi Mikel and Didider Drogba.
'I hope that Chelsea fans will finally see him come to the club. I’ll make sure I send him those text messages and calls, making sure Chelsea is his top priority, said Mikel.
'But it seems like he loves the club and wants to come to Chelsea. I’m sure he has all the big clubs wanting to sign him. I think if we can secure his signature it would be fantastic for the club.
'Didier is also speaking to him, sharing his own ideas and what the club means to us. We all want to see Victor come to the club. If it happens, it happens. It’s a huge transfer fee, but if we can match it and get him to the club that would be absolutely fantastic.'
Mikel was in the same Nigeria squad as Osimhen for the 2019 Africa Cup of Nations but it is unclear if Drogba and the striker have any prior connection.
Lukaku, 31, is still earning around £325,000 per week at Chelsea.
According to Capology, that makes him their joint-highest earner alongside Raheem Sterling - despite the fact he last played for the club in May 2022.
Lukaku won the Serie A title with Inter in 2020-21 when he was with the San Siro giants permanently and also reached the Champions League final with them on loan in 2022-23.