The France international was considered to be a marquee signing for Lyon when they spent big to lure him away from Bordeaux in 2010.
Gourcuff has, however, been hampered by injuries and struggled for form throughout his time at Stade Gerland.
Aulas concedes that the 26-year-old has failed to offer value for money and has hinted that Lyon may be willing to cut their losses.
Arsenal are among those to have been linked with Gourcuff in the past, and the door has now been opened for interested suitors to put a bid on the table ahead of the winter transfer window.
"He needs to win back his position in the team after his knee injury," Aulas told Lyon Capitale.
"We hope he'll be in the squad for the Marseille trip. If he comes back, if he has good offers and if he wants to leave, we could sell him.
"We made a huge investment to sign him when he was the best French player.
"For now, we can't say this investment hasn't been economically interesting."
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