Gourcuff, who has started just seven Ligue 1 matches this season, made a big-money switch to Lyon from Bordeaux in 2010.
Lyon paid €22 million for his services but have been frustrated ever since, with a string of injuries interrupting his time at the club.
The 27-year-old has not played for France since June and feels the time is right to move on – claiming he is left on the bench too often by manager Remi Garde.
Speaking about his refusal to sign a new deal, Gourcuff told L'Equipe: "I will let my lawyer handle it.
"An extension must be a sign of confidence from both parties, with everyone being satisfied.
"That fact that I've been injured regularly or often on the bench... I don't think it's relevant. I have not felt huge confidence from the club at times.
"Sometimes I find myself on the bench, like recently against Toulouse and Bastia. These are small signs. It does not hurt me but I take note."
Lyon sit 10th in the Ligue 1 table, with just six wins from their first 18 matches of the season.
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