The 22-year-old has repeatedly been linked with a move to the Gunners this summer.
"I know Lyon have refused an offer from Arsenal," the French international told Le Parisien. "Of course it's flattering that clubs are interested in me."
Grenier signed his first professional contract with Lyon in 2009 after graduating from the club's youth academy.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Liverpool | 15 | 11 | 3 | 1 | 31 | 13 | 18 | 36 |
| 2 | Chelsea | 16 | 10 | 4 | 2 | 37 | 19 | 18 | 34 |
| 3 | Arsenal | 16 | 8 | 6 | 2 | 29 | 15 | 14 | 30 |
| 4 | Nottingham ForestNott'm Forest | 16 | 8 | 4 | 4 | 21 | 19 | 2 | 28 |
| 5 | Manchester CityMan City | 16 | 8 | 3 | 5 | 28 | 23 | 5 | 27 |
| 6 | Bournemouth | 16 | 7 | 4 | 5 | 24 | 21 | 3 | 25 |
| 7 | Aston Villa | 16 | 7 | 4 | 5 | 24 | 25 | -1 | 25 |
| 8 | Fulham | 16 | 6 | 6 | 4 | 24 | 22 | 2 | 24 |
| 9 | Brighton & Hove AlbionBrighton | 16 | 6 | 6 | 4 | 26 | 25 | 1 | 24 |
| 10 | Tottenham HotspurSpurs | 16 | 7 | 2 | 7 | 36 | 19 | 17 | 23 |
| 11 | Brentford | 16 | 7 | 2 | 7 | 32 | 30 | 2 | 23 |
| 12 | Newcastle UnitedNewcastle | 16 | 6 | 5 | 5 | 23 | 21 | 2 | 23 |
| 13 | Manchester UnitedMan Utd | 16 | 6 | 4 | 6 | 21 | 19 | 2 | 22 |
| 14 | West Ham UnitedWest Ham | 16 | 5 | 4 | 7 | 21 | 29 | -8 | 19 |
| 15 | Crystal Palace | 16 | 3 | 7 | 6 | 17 | 21 | -4 | 16 |
| 16 | Everton | 15 | 3 | 6 | 6 | 14 | 21 | -7 | 15 |
| 17 | Leicester CityLeicester | 16 | 3 | 5 | 8 | 21 | 34 | -13 | 14 |
| 18 | Ipswich TownIpswich | 16 | 2 | 6 | 8 | 16 | 28 | -12 | 12 |
| 19 | Wolverhampton WanderersWolves | 16 | 2 | 3 | 11 | 24 | 40 | -16 | 9 |
| 20 | Southampton | 16 | 1 | 2 | 13 | 11 | 36 | -25 | 5 |
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