The Serie A side reportedly approached OL with a view to signing Gonalons, 24, last summer only to be turned down. Gonalons also stated his intention to remain at the club where he has emerged from the youth academy to lead the first team under coach Remi Garde.
However, Napoli boss Rafa Benitez is a firm fan of the creative yet combative midfielder, who has six caps for France, and is ready to step up his interest.
Negotiations between the two parties have reportedly already started with an initial fee of nine million euros sweetened by a potential two million euro bonus depending on Gonalons' performance in Italy.
Lyon president Jean-Michel Aulas, who has previously stated his determination to build the club's future on homegrown talents such as Gonalons and Clement Grenier, is due to meet his captain to discuss the feasibility of a winter move.
Talking to beIN SPORT in November, Gonalons said he felt he would "finish the season at Lyon" and told the press at his club's training ground on Monday he remained focused on squeezing OL into the top five after a poor start to the season rather than pondering what the January window might bring.
"I think it's the same for all the clubs," he said. "They're periods that clubs don't like too much, particularly the winter window which is difficult to cope with. But we players don't think too much about it. We all have a common objective, which is to climb up the table and achieve our goals come the end of the season, that's what's important."