The Blues have already spent just under £200m this summer on 12 players, with Pedro Neto the latest to walk through the door after his £54m move from Wolves.
Mail Sport previously reported that Chelsea have been offered Osimhen as part of a swap deal involving out-of-favour striker Romelu Lukaku.
The Sun have now reported that Napoli boss Antonio Conte wants two players and £39m in return for Osimhen.
It’s claimed that he wants Lukaku – who joined for £97.5m in 2021 – and young £17m midfielder Cesare Casadei plus £39m to seal the transfer.
Talks have been ongoing for a number of days over the future of Osimhen.
Giovanni Manna, Napoli’s sporting director, has been in London for talks with Chelsea about a potential swap.
He has explored potential moves for Manchester United’s Scott McTominay and Brighton’s Billy Gilmour.
Casadei meanwhile is a player that Chelsea could potentially throw in the mix for Osimhen, along with Lukaku – who has spent the last two seasons on loan in Italy with Inter Milan and Roma.
Napoli confirmed earlier this month that Osimhen asked to leave the club after he was left out of their Coppa Italia squad to face Modena.
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.
Enzo Maresca’s side are keen to sign another attacking player despite the arrival of Neto.
A move for Samu Omorodion from Atletico Madrid appeared to fall through, which in return stalled the sale of Conor Gallagher to head in the opposite direction.
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 Didier 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.’
Osimhen has also previously been linked with a move to Paris Saint-Germain, after the French side lost star striker Kylian Mbappe to Real Madrid this summer.
Lukaku failed to meet expectations following his return to Stamford Bridge in 2021 and Chelsea are keen to let him go.
Casadei, 21, has rarely featured since he signed for Chelsea in 2022. He was on loan at Leicester for part of last season where he worked with new Blues boss Maresca.