The 27-year-old midfielder has failed to live up to the high expectations which followed his £19 million move to the Ligue 1 giants three years ago and has often been linked with a move to the Gunners.
|4/7||Arsenal are 4/7 with Paddy Power to finish in the Premier League top four
"Can you see us paying part of his salary for him to play against us with another French club? We've never considered that and it would even more stupid now than it was a fortnight ago," Aulas told L'Equipe.
"All that I know, if I understood correctly, is that he was ready to lower his salary to go to Arsenal but that's not the same thing."
Arsenal had previously shown reported interest in Gourcuff's team-mate, Clement Grenier, earlier this summer before the Frenchman commited his future to Lyon.
Gourcuff, who has two years left on his current deal at the Stade de Gerland, scored a goal and contributed two assists in his side's 4-0 win over Nice, their first game of the Ligue 1 season.