However, the possibility of a part-exchange remains on the cards, with Aulas acknowledging that they are keen on signing Giroud, who will reportedly be allowed to leave the Emirates Stadium this summer.
Aulas told L'Equipe: "There's been an approach at some point for Giroud. He is a boy we like, who scores lots of goals and who has a lot of ambition for Russia."
Giroud made just 14 starts in the Premier League and Champions League last season, but he still managed a total of 14 goals.
It has also been claimed that West Ham United are keen on his signature, with the Hammers willing to meet an alleged asking price of £20m.