The Nigeria international has been linked with a move away throughout the summer window despite only signing a new Napoli contract in December.
Napoli seemingly agreed a new contract to protect Osimhen's value rather than tying him down for the long-term future.
However, Osimhen's new contract contains a £113m release clause which has seemingly put off many of his potential suitors.
Chelsea are one of those who may find it difficult to meet Napoli's financial demands, but they are hoping to come to a compromise by negotiating a swap deal.
Chelsea making progress in Osimhen, Lukaku swap deal
According to The Independent, Chelsea and Napoli are close to reaching an agreement over a deal which would see Osimhen head to Stamford Bridge with Romelu Lukaku replacing the 25-year-old at the Stadio Diego Armando Maradona.
The report claims that Osimhen could join on an initial loan deal with an option to buy, while Lukaku is expected to complete a permanent move to Napoli.
Although progress is being made, there is a belief that the potential swap deal may not be officially completed until the final week of the transfer window.
Chelsea are willing to be flexible in their usual strict wage structure, but they are in 'complex' discussions over how to structure Osimhen's wages, with the striker demanding £12m-per-year net.
The Blues are seemingly confident that they can finalise a move despite speculation suggesting that Osimhen is not excited by the prospect of joining Enzo Maresca's side.
A suitable move for both clubs
If Chelsea are able to pull off the move, it would represent a significant statement for a club who will want to improve upon two underwhelming Premier League seasons.
Osimhen would add undoubted quality to Chelsea's frontline, having scored 41 goals in 57 Serie A appearances over the last two seasons.
From Napoli's perspective, they are seemingly content with offloading the 25-year-old due to his significant wage packet.
New Napoli boss Antonio Conte is also keen to reunite with Romelu Lukaku after the pair previously worked together at Inter Milan.
Under Conte's watch, Lukaku scored 24 goals in 36 appearances during the 2020-21 season to help Inter claim the Serie A title.