Wenger is keen to bring in the France star should Cesc Fabregas leave the club this summer.
Fabregas has asked for a move to his boyhood club Barcelona.
An Arsenal source told The Sun: “While every effort is being made to keep Cesc at the club the boss is working towards an alternative.
“He believes Gourcuff’s finesse and grace will fit perfectly to Arsenal’s way of playing and will make it an almost seamless transition if Cesc does go.”
Gourcuff is expected to be a key player for France in the World Cup this summer and has a £21.8million get-out clause in his £80,000-a-week contract at Bordeaux.
