The Premier League side attempted to sign the 26-year-old last summer, but were unable to conclude a deal.
However, it appears he may be available this winter, with the Ligue 1 club in financial peril.
Due to this, the club’s president Jean-Michel Aulas confessed a number of players may have to make way to balance the books:
“We’re planning to sell two or three players for a total of €30million.” Aulas said.
He also admitted that Gourcuff may be one of those sold:
“If he (Gourcuff) returns to the highest level and he wants to go, then there could be a transfer.”
This news will delight Arsene Wenger who has been tracking the Frenchman for the past few seasons.
Gourcuff was once regarded as one of the finest talents in Europe, but a succession of injuries have halted his development.
He shot to fame during the 2008/09 season with an impressive loan spell at Bordeaux.
The move from parent club AC Milan was made permanent the following year and more impressive displays tempted Lyon to splash €22m for his signature in 2010.
Since then he has struggled with ankle injuries and lost his position within the French national set-up.
However, his creative quality is still evident which may tempt the North Londoners to make a January swoop.