The 26-year-old has scored one goal in eight appearances for Lyon this season and has struggled to hold down a regular first-team place.
Gourcuff rose to prominence at Rennes before moving to AC Milan, however he struggled at the San Siro and returned to France in 2008, joining Bordeaux.
After winning the Ligue 1 title in 2009, he moved to Lyon but has failed to replicate his impressive performances.
Arsène Wenger has previously admitted his interest in the midfielder, with the Gunners boss reportedly enquiring about Gourcuff before he joined Lyon.
However, Lyon chairman Jean-Michel Aulas is unaware of any offer from the north London side.
“Arsenal and Gourcuff? I don’t know about any offers,” said Aulas. “I have never spoken with Arsenal.”
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