The Nigeria international has spent the last four years in Naples, scoring 76 goals in 133 competitive appearances.
Osimhen played a key role in Napoli's Serie A title triumph in 2022-23, cementing his legacy at the Stadio Diego Armando Maradona.
However, Osimhen has made no secret of his desire to try a fresh challenge and is looking to leave the Serie A club before the summer transfer deadline.
Napoli had previously insisted that Osimhen's potential suitors needed to be paid in full, but they have dropped their price demands as they look to find a resolution to his current situation.
Antonio Conte's side are already starting to move on from Osimhen and are on the verge of signing Chelsea's Romelu Lukaku as his replacement.
Chelsea handed boost in Osimhen pursuit
Chelsea were believed to be keen to use Lukaku in a bid to sign Osimhen in a swap deal or a part-exchange agreement.
Their hopes of signing Osimhen appeared to suffer a significant setback after it emerged that Napoli were close to agreeing a deal to sell the striker to Saudi Pro League's Al-Ahli for €45m (£38.1m).
However, the Blues have been given renewed hope by Osimhen's agent Roberto Calenda, who made it clear that his client is not interested in joining the Saudi Pro League.
As per Get Football News Italy, Calenda said: "Osimhen is a Napoli player, with a contract recently renewed to our mutual satisfaction. He made history in blue and when there were important offers (this year too) we always accepted the club's decisions.
"As I have already said, he is not a package to be sent far away to make room for new prophets. Victor was elected African Footballer of the Year, eighth in the Ballon d'Or, he still has a lot to say in Europe. Respect and balance are needed."
Why are Chelsea interested in Osimhen?
Chelsea demonstrated in Sunday's dominant 6-2 win over Wolverhampton Wanderers that they already boast considerable firepower in their side.
While they may boast an array of attacking talent, the Blues are still keen to bolster their squad with the addition of a centre-forward.
Chelsea's current strike options include Senegal international Nicolas Jackson and 18-year-old Marc Guiu, who arrived from Barcelona earlier this summer.
The Blues also have Armando Broja, Deivid Washington and David Datro Fofana on their books, but there is a possibility the trio could all be moved on ahead of Friday's transfer deadline.