The Frenchman has enjoyed a fine season at Olympique Lyonnais and his performances have attracted the attention of Gunners boss Arsene Wenger
Gunners boss Arsene Wenger admitted on Sunday that he was interested in the attacking midfielder, who has enjoyed a breakthrough season at Stade Gerland.
"Clement said to me that he will give priority to Lyon if we qualify for the Champions League. So I prefer [to listen to] what he said, rather than what Arsene Wenger said," Aulas told Canal+.
"But, we have to make a financial effort to keep him. We will see after the level of our effort [that we have to do].
"If Arsene wants to have an idea of Grenier's price, I will tell him that it is the same as what Bayern Munich paid for Mario Gotze - around €37."
The Gunners are keen to strengthen their squad this summer after securing Champions League football ahead of local rivals Tottenham on the final day of the season.
There has been talk of Wenger having up to £70 million to spend with the likes of Steven Jovetic, Wayne Rooney, Sebastien Corchia as well as a potential new goalkeeper all on the radar.