Gonalons was reportedly set to sign for the Serie A side, who had previously displayed interest in the close-season, only for Lyon chairman Jean-Michel Aulas to reject an offer believed to be worth €17million on Monday.
The 24-year-old Lyon captain's representative Frederic Guerra confirmed that personal terms had been agreed when Aulas opted not to do business with Napoli.
And Guerra has not ruled out the possibility of a transfer at the end of the season.
"Everything was OK (for the transfer)," Guerra told RTL.
"I was approached by Napoli last summer, they had offered €9m for Maxime, they absolutely wanted the player, who had affected (Napoli coach Rafael) Benitez since scoring for Lyon against Liverpool in the (UEFA) Champions League.
"The offer climbed to €15m and we found it very interesting. We agreed to the move and Maxime was happy to move to the Azzurri, he liked the project and everything was alright.
"The player would have been going to an ambitious team whilst also improving his salary.
"Napoli is third in the Italian championship and should, in principle, play in the Champions League next season, which doesn't seem to the case with Lyon (10th in Ligue 1).
"So there was both a sporting project and a financial incentive.
"(Lyon) took the decision to retain Maxime. However, a future departure is not excluded.
"There will be no tug-of-war with Lyon, Maxime knows the situation of the team and the club in which he grew up."
