Reports in France and Italy have claimed that Gonalons is a major summer transfer target for Napoli, and a fee in excess of €12million (£10.2m) had been mooted.
However, Lyon have released a statement to dismiss the latest speculation and have reaffirmed their intention to hang on to Gonalons.
"Olympique Lyonnais were surprised to learn, by reading L'Equipe, that a fee has been defined for the sale of Maxime Gonalons and that this would be more than €12m," read a statement on the club's official website.
"Remember, the club has no intention to give up its captain.
"The club's development strategy is clear - Gonalons is one of the most promising young players.
"No clubs have contacted us, especially Napoli, and the club is sorry about the fact that some say to the contrary."
Napoli will now reportedly look at alternative targets as the Serie A side also close in on the signing of PSV Eindhoven winger Dries Mertens, who underwent a medical on Saturday.