Gourcuff has been linked with the Gunners for the past 12 months and there were suggestions Wenger was hoping to lure the 25-year-old to the Emirates in the New Year.
However, the Arsenal boss says he is not a transfer target although he admits he is a fan of the Lyon man.
"He is a player I like a lot and I believe people have been very critical towards him in France," Wenger told Canal+."However, we won't be in the winter market for any midfield positions considering that our players are back from injuries."
Gourcuff himself has always maintained he is happy at Lyon and is just concentrating on impressing in the second half of the season in order to get into the France squad for Euro 2012.