The 22-year-old has been on loan with the Ligue 1 side this season after failing to make an impact since joining the Rossoneri from Rennes in 2006.
“I want to stay with Bordeaux,” he stressed emphatically. “Now it’s just up to the directors to come to an agreement.”
Gourcuff won the Player of the Season award at Bordeaux.
Bordeaux will have to find around £12million to buy the playmaker, something that seems very unlikely they will manage.