France midfielder Gourcuff was believed to have been a long-term target for Arsenal manager Arsene Wenger before the player moved from Bordeaux to Lyon last August.
Wenger's quest to find replacements for the departed Cesc Fabregas and Samir Nasri this summer took him all the way up to deadline day on Wednesday, when he eventually succeeded in buying Mikel Arteta from Everton and loaning Yossi Benayoun from Chelsea.
However Aulas revealed that he rejected an enquiry from Arsenal for 25-year-old Gourcuff, yet to play this season due to an ankle injury, on Tuesday.
"I got a call on the penultimate day of the transfer window from (Arsenal scout) Gilles Grimandi asking for a loan," Aulas told RMC Sport. "We believe in re-establishing Yoann. He has been operated upon. He has just resumed training.
"We have chosen Gourcuff, like last year. It was hard last season. Hopefully he will demonstrate his capabilities this term."
Gourcuff was a key part of the Bordeaux side which won the Ligue 1 title in 2009, but his move to seven-times champions Lyon last term saw him struggle to replicate that form.