The 26-year-old spent last season on loan with the Turkish giants, where he scored an impressive 37 goals and provided seven assists in his 41 games.
Galatasaray remain adamant in their pursuit of making that move permanent, but as of yet, have been unable to agree terms with Napoli.
Napoli are understood to be holding out for Osimhen’s €75 million release clause and are unhappy with the terms they’ve been offered by Galatasaray.
Their offer matches the asking price, but it would be paid in instalments rather than outright, and President Aurelio De Laurentiis is now making more demands.
According to AS, he wants specific payment instalments, along with a '20 per cent stake in Osimhen's subsequent signing and a guarantee that the player would not be sold to Italian clubs for three years'.