The French international has long been rumoured for a switch to Arsenal, with Gunners manager Arsene Wenger a known admirer of his ability.
However, agent Jean-Pierre Bernes has quashed rumours of a transfer.
"We talked about that," Bernes told France Football. "It would be nonsense to leave.
"I can't see any benefit to finding a new club three months before Euro ."
Gourcuff has previously played for Bordeaux and AC Milan.