The former Rennes and Valencia right-back, 33, has been at Lyon for a decade but his current deal is set to expire this summer.
Yet with his powers far from waning, boss Remi Garde said he would be entering talks regarding an extension.
“A meeting has been scheduled for next week with his agent to start talks,” Garde said.
“I have made him part of my plans and would like him to stay here.
“Right now there is the economic element that needs sorting out – it is up to him whether he wants to continue with our project, or look abroad. I hope he stays.”
Reveillere has made over 200 Ligue 1 appearances for Les Gones, winning 19 France caps in the process.