The Nigeria international is one of the hottest properties on the European market after leading Napoli to the 2022-23 Serie A title with a league-high 26 goals last season.
Osimhen also provided five assists and netted five times in the Champions League to take his total for Napoli to 59 goals and 14 assists from 101 matches since joining from Lille in 2020.
The 24-year-old's Partenopei terms now only have two years left to run, but president Aurelio de Laurentiis previously insisted that the Italian champions had no reason to sell him this summer.
However, the Napoli chief has now confessed that Osimhen could depart if an interested party makes an offer that they cannot refuse, and their asking price is thought to be north of £100m.
Manchester United and Chelsea have been persistently linked with moves for Osimhen this summer, but the Blues have already signed Christopher Nkunku from RB Leipzig and are also finalising a deal for Villarreal's Nicolas Jackson.
Meanwhile, Man United fear being priced out of a swoop for Osimhen, and the Red Devils' slow takeover process is also harming their chances of getting deals done early in the transfer window.
With the Premier League duo seemingly out of the picture for the time being, journalist Alfredo Pedulla claims that PSG are now preparing to make a formal approach for the former Lille man.
Pedulla reports that PSG are set to offer as much as €120m (£103.2m) to €125m (£107.5m) up front, which could rise to as much as €140m (£120.4m) to €150m (£129m) with performance-related add-ons.
Rumours that PSG were ready to offer as much as €180m (£154.8m) for Osimhen are believed to be wide of the mark, but the French champions are waiting patiently to hear the outcome of a meeting between De Laurentiis and the Nigerian's agent, where Napoli could still offer Osimhen a new deal.
PSG have freed up a large chunk of their wage bill through Lionel Messi's exit on a free transfer to Inter Miami, and the Parisiens could raise significant funds through the sale of Kylian Mbappe.
The 24-year-old has informed PSG that he will not be activating the extension option in his contract, meaning that he could leave the club for nothing at the end of next season, a scenario which Les Parisiens are desperate to avoid.
PSG are supposedly trying to offload Mbappe this summer following his bombshell letter, but the France international has insisted that he wants to stay at the Parc des Princes and will make a decision on his future next year.
While the Mbappe saga continues to rumble on in the background, PSG are expected to confirm the signings of Inter Milan defender Milan Skriniar, Real Madrid attacker Marco Asensio and Sporting Lisbon midfielder Manuel Ugarte next month.
The French champions are also working on moves for Mallorca's Lee Kang-in and Benfica's Cher Ndour, while Luis Enrique is expected to take over as the team's new head coach ahead of Christophe Galtier's anticipated sacking.