The France playmaker has not enjoyed the most distinguished spell at Stade Gerland, with injuries plaguing much of his stay, and Arsene Wenger is understood to be an admirer of the talented forward.
But Lyon chairman Jean-Michel Aulas has now quashed talk of Gourcuff making a move to north London.
"Arsenal and Gourcuff? I don't know about any offers," Aulas told BeIN Sport.
"I have never spoken with Arsenal."
With Lyon having previously revealed that they would be willing to part with key players in January in a bid to free up funds, the speculation may not disappear.