The 27-year-old is also thought to be a transfer target of Arsenal and has been strongly linked with a move away from the Ligue 1 club after an injury troubled last season, in which he scored just three goals in 18 league appearances.
Despite the fact he has failed to replicate the form he showed at Bordeaux since moving for 22 million euros in 2010, Lyon is still keen to keep him at the Stade de Gerland.
The club's presidential adviser Bernard Lacombe told OL TV: "Yoann Gourcuff won't leave during this transfer window. The president told me that there were opportunities, but all three parties need to be in agreement.
"The president has had, it's true, a lot of approaches, and that has enabled him to have a different point of view other than OL's and he's talked about it with Yoann. But I don't think he'll leave."
Gourcuff started his career with Rennes before having spells with AC Milan and Bordeaux prior to his move to Lyon. The attacking midfielder has also made 29 appearances for France since winning his first cap back in 2008.