Arsenal, who are understood to be long-time admirers of the France international, are once again being credited with holding an interest.
Lyon have admitted that they are open to offers for their most saleable assets, with their recruitment plans dependent on moving players on.
Gourcuff, who has struggled for form and fitness throughout his time at Stade Gerland, was believed to be among those most likely to be offloaded, but Lyon claim he will remain with them until the summer at least.
Club president Jean-Michel Aulas told tuttomercatoweb.com: "Until June he will definitely remain here, then we will discuss his future.
"He has been injured and this is not the time to talk about a move to another club."