Emirates club missed out then but could succeed in the future.
Arsenal had a £22million offer rejected by Lyon for midfielder Yoann Gourcuff last summer, according to the French club’s president.
The Gunners wanted the 25-year-old to replace Barcelona-bound Cesc Fabregas and provide the creative spark to their midfield.
The France international has been on manger Arsene Wenger’s radar for some time with the boss failing to land his signature in the past.
But Lyon president, Jean-Michel Aulas, claims he turned down a fresh bid for Gourcuff in the last transfer window.
“There was a request from Arsenal and I said no,” Aulas told L’Equipe. “He has a five-year contract, wants to succeed with Lyon and I believe him.
Gourcuff did not enjoy his best campaign last season as he was troubled by injury.
But Aulas has hinted he may be ready to sell the playmaker as he needs to balance his books.
“To be totally financially secure, it may be necessary to sell a player in the winter transfer window,” he told Le Progres.
This may tempt Wenger with another bid in the January window, but Lyon will only sell if they are knocked out of the Champions League by then.