The 27-year-old France midfielder is reportedly keen to leave Lyon, and Arsenal have been strongly linked.
Gervinho had been the subject of a £6.9m offer from Roma - the Ivorian played under Roma coach Rudi Garcia at former-club Lille.
But Lyon are believed to be interested in bringing Gervinho back to France, and are currently mulling a bid of their own.
Arsenal's interest in Gourcuff dates back several years to when the France international was at Rennes. He's since endured a difficult spell in Italy with AC Milan, but returned to Ligue 1, initially with Bordeaux and now with Lyon.
But the creative playmaker is thought to be keen to test himself elsewhere.
The Gunners have space in the squad for a new midfielder, and Gourcuff would certainly strengthen their ranks.
Abou Diaby remains a long-term injury concern, while Francis Coquelin has been allowed to join German side Freiburg on loan for the season.
That leaves Mikel Arteta, Jack Wilshere, Aaron Ramsey, and Tomas Rosicky as Arsene Wenger's midfield options.