The French midfielder has been linked with the Gunners for a number of years, with Arsene Wenger having tracked his career from the beginning.
Speculation had suggested that 26-year-old, who has struggled with off-field problems and injuries in recent years, could move to North London for as little as £3m, but Aulas has rubbished the talk.
"Arsenal and Gourcuff? I do not know anything about an offer", Aulas told beINSport.
"I have not had any discussions with Arsenal. And we have not offered him to Spartak Moscow, this is not true."
Gourcuff has previously played for Rennes, AC Milan and Bordeaux before current side Lyon.