According to reports in the Sun, the Frenchman was close to making a £20 million bid for his compatriot, but was frightened off by revelations that the 25-year-old midfielder needed a knee operation.
Wenger revealed: "I was interested. Then I learned of his medical condition."
However, this will not be the end of Arsenal's interest in the France midfielder, as further reports indicate that the Arsenal manager is still considering another bid in January for Gourcuff.
The Frenchman was just one of the players chased by the Gunners in the final days of the transfer window as Arsenal searched for replacements for Samir Nasri and Cesc Fabregas, finally settling on Mikel Arteta and Yossi Benayoun instead.
Gourcuff is regarded as one of the best attacking midfielders in France and is thought to be a long-term target of several top sides.
The Lyon star scored three goals in 27 Ligue 1 appearances last season.