The Nigerian forward has been heavily linked with a move away from Napoli due to serious interest from the Premier League, combined with his exploits in Serie A.
A host of Premier League sides are keen, including Manchester United and Newcastle, two clubs in the market for a goalscorer in the summer.
Napoli are aware of the interest Osimhen has been attracting and it has been claimed their hierarchy held a behind closed doors meeting on Wednesday to decide the next course of action.
The Serie A giants have set a high asking price for him and according to the Italian daily Corriere dello Sport, they do not want to offer any discounts.
Napoli are claiming to be asking for a fee of €110m before agreeing to sell the forward in the next transfer window.
The striker has more than three years left on his contract and Napoli are under no pressure to accept a lesser offer.
The 23-year-old forward has scored 16 times in all competitions for the Serie A giants this season.