Arsene Wenger is known to be an admirer of the 22-year-old playmaker, who saw his efforts in 2012/13 rewarded with senior international recognition with France.
A summer move away from his homeland has been widely touted, especially as Grenier has just 12 months left to run on his current contract.
Arsenal were hoping to use that situation to their advantage, but have failed with an initial approach.
Grenier admits he does not know what the rest of the summer will hold, with contract discussions due to be held and further offers from abroad expected.
He told Le Parisien: "I know Lyon have rejected an offer from Arsenal. Of course it is flattering that clubs are interested in me.
"It's hard for me to talk about my future now because I'm not yet certain of it. I prefer to wait to be 100 per cent sure of what is going to happen before I do it."
Grenier went on to tell RTL that he is due to have a meeting with Lyon coach Remi Garde and chairman Jean-Michel Aulas after the squad return from a pre-season training camp in the Alpine resort of Tignes on Friday.
He said: "My decision will be made and announced after the meeting. As soon as I'm 100 per cent certain, then I can say more about it. Even for me it's a little complicated.
"I'm very happy to return to Tignes, to prepare. I know the season will be long. That's my priority for the moment."