Wenger has been tracking Gourcuff for some time and was left bitterly disappointed when the talented playmaker rejected a move to Arsenal in 2006, leaving Rennes for Milan instead.
However, since his move to the San Siro, Gourcuff has struggled to break into the first team, playing just 21 times last season and finding himself confined to the substitutes bench this campaign.
Nevertheless, should Gourcuff be allowed a move to the Emirates next month, Milan would still demand a considerable fee.