The midfielder has struggled at the Ligue 1 side since his arrival in 2010, with injuries hampering his playing time, and reports that suggested that Arsene Wenger would offer him a fresh start.
But Aulas told BeIn Sport: "Arsenal and Gourcuff? I don't know about any offers.
"I have never spoken with Arsenal."
The chairman did confirm, however, that Serie A giant Juventus had been rebuffed in a bid for striker Lisandro Lopez. Though Lyon had admitted earlier in January that the club may be willing to part with some of its key men, Aulas is convinced that the Argentine is staying put.
"There was an offer but it didn't match our valuation or the desire of the player," he confirmed. "We can forget about that."