The 26-year-old French international has long been linked with a switch to north London, as the playmaker looks to get his career back on track, after an injury-ravaged spell at Stade Gerland.
Gunners boss Arsene Wenger is a known admirer of Gourcuff, and the Emirates Stadium has been touted as the ideal location for the Ligue 1 star to rediscover his form.
However, despite admitting to being a fan of the Lyon midfielder in the past, no deal has been discussed to bring the player to the Premier League during the January transfer window.
"Arsenal and Gourcuff? I don't know about any offers," Aulas told BeIN Sport. "I have never spoken with Arsenal."
Lyon are having to fend off speculation of interest from a number of clubs about a variety of players after the French club recently revealed that they would be willing to part with key men this month, in an effort to free up some funds for new signings of their own.