Newcastle United and Arsenal have been linked with a move for the 23-year-old, and the Magpies reportedly had a bid of £8m knocked back by Lyon in January after they sold Yohan Cabaye to Paris Saint-Germain.
The Ligue 1 side reportedly value Grenier at closer to £15m, and the midfielder said that he is not sure if he will still be at the French side next season.
He is quoted as saying in the Evening Chronicle: "You never know what can happen. I think first I have to prepare myself.
"I'm at Lyon, but I know that economic reasons may change that. If it happens then it will, in any case, be a decision made together."
Grenier was forced to pull out of France's World Cup campaign due to injury.