The 21-year-old has been linked with a move to Campania for several weeks, and recent reports stated he visited the club’s training facilities as they looked to push a deal over the finish line.
Sport Mediaset reports that visit looks to have paid off, as Napoli sporting director Cristiano Giuntoli is in Sardinia where a deal could be wrapped up as soon as Tuesday evening.
The report states the Azzurri will pay €81m for the Nigerian striker, though Corriere dello Sport states the deal will be in the region of €50m plus Adam Ounas in order to reach that figure.
Osimhen will sign a contract that pays him €5m a season, with a medical and announcement coming as soon as Thursday.
The transfer would seal a second major sale in two seasons for Lille, who sold Nicolas Pepe to Arsenal last summer for €80m.