However, the 22-year-old insists that for the moment he is focused on giving his all for the former French champions.
"Things move quickly in football, I'm aware of that," he told Lyon Capitale. "I don't want to go back over what happened with Nice. It's in the past. I've talked about it with quite a few people at the club.
"It was a tricky period, difficult to cope with, but it helped me grow. I've matured still further. I've always had - more or less - a career plan. When you know where you want to go, you need to establish it, and do everything you can to get there.
"I'm already fortunate to be at a big club. For me, the most important thing is to always improve. If one day I have to leave, because it's time to, then I'll do it. For the moment, though, my sole objective is to get back to my best form with OL."
Grenier's current contract with Lyon runs out in the summer of 2014.