Despite having recently penned a contract extension at Stadio Diego Armando Maradona, it is an open secret that Osimhen could move elsewhere during the summer transfer window.
However, possessing a release clause in the region of £109.5m, the race for the Nigeria international's signature could be drawn out.
In recent weeks, the perception has been that only Paris Saint-Germain have been prepared to spend big money on the 25-year-old.
Although the Ligue 1 giants have not been keen to meet the option in the player's contract, there is a acknowledgement that they will have to pay a cast sum to get a deal over the line.
Napoli stand firm
According to Calcio Mercato, Napoli president Aurelio De Laurentiis currently has no interest in parting ways with Osimhen for anything below his release clause.
On Monday, there are said to have been further developments with Roberto Calenda - the representative of Osimhen - flying to Paris for discussions.
A call was also allegedly held between De Laurentiis and PSG chairman Nasser Al Khelaifi, as well as sporting directors Giovanni Manna and Luis Campos.
Nevertheless, it appears that the meetings were not productive with PSG stating that they are unwilling to pay nearly £110m for a new centre-forward.
The report adds that Napoli have refused the opportunity to sign either Nordi Mukiele, Carlos Soler or Lee Kang-in in part-exchange.
As a result, an impasse has been reached, leaving the realistic prospect of a proposed transfer being scrapped and the likes of Arsenal, Chelsea and Manchester United coming back to the table.
Why development is bad news for Chelsea
Chelsea would love to add Osimhen to Enzo Maresca's squad, even if it was purely to sign a proven number nine to compete with Nicolas Jackson.
The scenario is complex, though, with Chelsea hoping that Napoli will take Romelu Lukaku off their hands on a permanent basis.
That is only possible if Osimhen is sold, putting the West Londoners in a position where they face further obstacles to get the Belgium international off their wage bill.