Negotiations are ongoing between the clubs, with the Serie A side hoping to sign Romelu Lukaku from the Blues and the Premier League team hoping to get Osimhen to move the other way.
The Athletic report that, if deals are to be done, then Lukaku moving to Napoli would be a permanent transfer while the likelihood is that Chelsea would bring in Osimhen on loan with an option to buy.
Napoli are very keen to snap up Lukaku and see the Belgian striker reunite with new manager Antonio Conte after their successful, title-winning time together at Inter Milan.
The 31-year-old appears to have no future at Chelsea and is hopeful that he can return to Italy after spending last season on loan at Roma.
Osimhen has come to an agreement with Napoli that he will leave the club this summer, but a deal is proving complicated to come to.
Paris Saint-Germain want to sign the Nigeria international but are not willing to meet the release clause in his Napoli contract, which stands at €130m (£109.5m).
Arsenal are also interested and talks have been held, but the Gunners are also not going to meet the forward’s huge release clause.
Chelsea may win the race to sign Osimhen and do so on an initial loan move, although other interested parties may also fancy going down that route.
Osimhen has not been involved in pre-season with Napoli as Conte revealed that the striker has agreed with the club that he will move on this summer.
‘I know that there are agreements with the club, it’s a totally different situation, which I’ll witness,’ Conte said.
‘Then if you ask me about the player, he’s a top player, but I can’t get into any discussions about Osimhen because these are previous agreements.’
