Gourcuff is currently on loan with the Ligue 1 side until the end of the season and would have to pay £13m to buy him outright.
“The Coach wants to keep Gourcuff and so do the directors,” Bordeaux chief Jean-Louis Triaud told Aujourd’hui Sport.
“The majority shareholders for the club have said that they will help us achieve our goals.
“The World Cup will take place next summer and France will probably qualify and Gourcuff will be in the team, so it’s probably not the best time for him to be unsettled.
“There are many arguments why Yoann should stay here at Bordeaux.”