For a number of transfer windows, the Nigeria international has been heavily linked with a move to Stamford Bridge, his alleged preference if he were to move to the Premier League.
With Osimhen scoring 26 goals on the way to Napoli winning last season's Serie A title, his valuation has only increased recently, helped by penning a contract renewal at the back end of last year.
However, penning fresh terms also brought a release clause into play, reportedly in the region of £113m with Napoli president Aurelio De Laurentiis protecting his club's position at the negotiating table.
Nevertheless, De Laurentiis has already acknowledged that he expects the 25-year-old to move to a new club after the conclusion of 2023-24.
Is a move to Chelsea realistic?
All things point to Chelsea being outsiders in the race for Osimhen at this stage, partly due to the Blues not featuring in next season's Champions League.
Participating in any European competition will be regarded as a bonus given that Mauricio Pochettino's side are in ninth position in the Premier League table and due to face Manchester City in the FA Cup semi-finals.
That said, it is their financial position that is more to their detriment, co-owners Todd Boehly and Clearlake Capital having spent in excess of £1bn across four transfer windows and desperately needing to recoup some funds to make further additions.
According to FootballTransfers, the Chelsea board intend to try to raise more than £170m in player sales to put them in a position to be able to afford Osimhen.
The first target must be meeting all Premier League financial rules at June 30, the next date for the latest accounts to be published, but further inroads need to be made in the long term.
How may Chelsea go about generating that level of money?
As has been suggested during the last two transfer windows, Boehly and Clearlake remain insistent on selling Gallagher, despite his influence in the squad.
The report adds that Trevoh Chalobah, Ian Maatsen and Armando Broja will also be sold, adding to the £28m that should be generated from Lewis Hall completing a permanent move to Newcastle United.
Maatsen and Broja are currently enjoying contrasting fortunes on loan at Borussia Dortmund and Fulham respectively, yet both players should attract interest in the summer.
football.london is also cited as claiming that the exits of Marc Cucurella, Thiago Silva and Malang Sarr will help matters, as will the permanent departures of out-of-favour Kepa Arrizabalaga, Romelu Lukaku and Hakim Ziyech.
In the case of Arrizabalaga and Lukaku, Chelsea ideally need to find a buyer before June 30 or else their lucrative wages will be added to the club's outgoings at a time when they cannot necessarily afford them to be.