Osimhen, a 21-year-old forward, and Gabriel, a 22-year-old defender, travelled from Lille, where they have resumed training, to Italy on Tuesday to start talks with Aurelio De Laurentiis, the Napoli owner and his sporting director, Cristiano Giuntoli.
The offer made by the Serie A club is split €70m for Osimhen and €30m for Gabriel, which meets Lille's asking price.
The two players are set to stay in the south of Italy for a few days, where they will hold talks with Napoli manager Gennaro Gattuso and a deal could be finalised quickly.
Two of the revelations of the 2019-20 Ligue 1 season, they are among the most coveted players in Europe this summer and Napoli are edging towards recruiting them, in what would be a great coup for the club.
Sources have told ESPN that he would prefer a move to the Premier League where he dreams of playing. Chelsea and Manchester United are two clubs interested in him but are yet to make an offer. However, sources have told ESPN that Napoli are confident they can convince him to move to Italy.