The French club are in a strong position to sign the 25-year-old, but negotiations have begun and are not progressing as PSG had hoped.
Fabrizio Romano reports that PSG are refusing to meet Osimhen's release clause, which stands at a huge EUR130m (PS109.
5m), and the Parisiens consider too much for the Nigeria international.
Napoli are happy to lower the price if PSG send a player in the opposite direction and reportedly asked for South Korean star Lee Kang-in to be included in a swap deal.
However, PSG have no intention of letting the 23-year-old they signed only last year from Mallorca leave and the suggestion was rejected.
Italian publication CalcioMercato states that the deal is 'at risk' as PSG came back with the idea of Carlos Soler and Nordi Mukiele being included in a deal, but Napoli were not interested.
While an agreement could still be reached, the two sides are at loggerheads and PSG are not desperate for the signing as they already have Goncalo Ramos and Randal Kolo Muani in their ranks.
The Blues reportedly dimmed their interest in the Nigerian earlier this summer, with a worry about his injury record and with his release clause considered too expensive.
Arsenal have also suggested they will not be spending as much as PS109.
5m on the forward.
There will be hope among all interested parties, though, that Napoli may end up accepting less than Osimhen's huge release clause as they have made an agreement with the player that the will be sold this summer.
Antonio Conte has taken over as Napoli manager this summer (Picture: Shutterstock) 'As far as Osimhen is concerned, just as I knew very well about the situation of Kvara, Di Lorenzo, Anguissa, Lobotka, on which I have placed an absolute veto,' Conte said last month.
'Having said that, I know what the situation is regarding Osimhen.
I know that there are agreements, that it is a situation different from all the others.
I can only assist.
'He is a player of the highest level, exceptional, but I cannot enter into any discussion because it is part of previous agreements which have been clearly stated to me.
'For more stories like this, check our sport page.
Follow Metro Sport for the latest news on Facebook, Twitter and Instagram.
MORE : Erik ten Hag warned Manchester United transfer decision could 'blow up in his face'MORE : Pep Guardiola issues major update on Kevin De Bruyne's Manchester City futureMORE : Mikel Arteta offers update on 'unbelievable' Arsenal star ruled out of US tour with injury.
Largest Football Social Network