The 22-year-old, who is being tracked by the Gunners, revealed he has already made a decision on his future but refused to confirm where he will be playing next season
Earlier in May, Arsene Wenger confirmed to Telefoot that he was monitoring the 22-year-old, likening the playmaker to former Gunners player Samir Nasri.
Lyon president Jean-Michel Aulas warned Arsenal they would need to pay £31 million in order to sign the Grenier this summer, but the in-demand midfielder has now confirmed he has made a decision on his next destination.
"Have I made a decision? Yes. More or less. I keep it for myself as I care for my discussions I have had with the president and the coach," Grenier told Le Progres.
"I just want to say that I've never had demands. Moreover, either with the club or with my advisors, figures were never mentioned. My choice is a sporting one."
Grenier, who has recently been called up to the France national team for les Blues' upcoming friendlies against Uruguay and Brazil in the absence of Nasri, insists he is unfazed by speculation surrounding his future and will not be perturbed by competitions for places at the Emirates Stadium.
"A fight between Arsenal and Lyon for me? Maybe. The competition at Arsenal? There is already that here [at Lyon]," Grenier continued.
"It is the same in all the major clubs and it is not a hindrance in my decision making. I'm still a young player. But I always set goals and do everything to surpass myself. Whether it is at Lyon or elsewhere.
"For now, I'm still a Lyon player and I may stay next season. I do not know myself what will happen. The only thing I expect is really at a sporting level, and my desire is to progress."