It has been suggested that Rafael Benitez has identified the 24-year-old as one of his main targets.
However, Lyon have moved quickly to make it clear that they have no intention of letting their captain leave the club this summer.
In a statement on the club's official website, Lyon said: "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.
"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."
Gonalons joined Lyon as a youth player in 1999 and has risen through the ranks to become one of the club's most important players.