Gourcuff has been courting the attention of several of Europe's top clubs following an impressive spell at the Les Girondins, with Premier League side Arsenal showing reported interest in signing the schemer.
The French international helped his side to the Ligue 1 title in 2009 but was unable to replicate the form this season that inspired them to glory the year previous.
The 23-year-old has still courted transfer interest, though, and has been widely tipped to leave Parc Lescure after returning from South Africa, where he is currently on World Cup duty with France.
But Lyon are unlikely to be one of the sides agreeing a deal for the playmaker, as Aulas revealed the transfer fee commanded by Bordeaux would be too high.
He said: "We are interested in Gourcuff because we think he is a very good player but we are not in the market for him as the price ranges from 25 to 30million euros (£25m)."