The 23-year-old was set to be part of the France squad at the World Cup, but was injured less than a week before the tournament started.
According to The Mirror, Arsene Wenger has been keeping an eye on Grenier's recovery and will make a bid for him if he is fit by the start of the season.
Grenier scored four goals for Lyon in Ligue 1 last season.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Liverpool | 21 | 15 | 5 | 1 | 50 | 20 | 30 | 50 |
| 2 | Arsenal | 21 | 12 | 7 | 2 | 41 | 19 | 22 | 43 |
| 3 | Nottingham ForestNott'm Forest | 21 | 12 | 5 | 4 | 30 | 20 | 10 | 41 |
| 4 | Newcastle UnitedNewcastle | 22 | 11 | 5 | 6 | 38 | 26 | 12 | 38 |
| 5 | Chelsea | 21 | 10 | 7 | 4 | 41 | 26 | 15 | 37 |
| 6 | Bournemouth | 22 | 10 | 7 | 5 | 36 | 26 | 10 | 37 |
| 7 | Manchester CityMan City | 21 | 10 | 5 | 6 | 38 | 29 | 9 | 35 |
| 8 | Aston Villa | 21 | 10 | 5 | 6 | 31 | 32 | -1 | 35 |
| 9 | Fulham | 22 | 8 | 9 | 5 | 34 | 30 | 4 | 33 |
| 10 | Brighton & Hove AlbionBrighton | 21 | 7 | 10 | 4 | 32 | 29 | 3 | 31 |
| 11 | Brentford | 22 | 8 | 4 | 10 | 40 | 39 | 1 | 28 |
| 12 | Crystal Palace | 22 | 6 | 9 | 7 | 25 | 28 | -3 | 27 |
| 13 | Manchester UnitedMan Utd | 21 | 7 | 5 | 9 | 26 | 29 | -3 | 26 |
| 14 | West Ham UnitedWest Ham | 22 | 7 | 5 | 10 | 27 | 43 | -16 | 26 |
| 15 | Tottenham HotspurSpurs | 21 | 7 | 3 | 11 | 43 | 32 | 11 | 24 |
| 16 | Everton | 20 | 3 | 8 | 9 | 15 | 26 | -11 | 17 |
| 17 | Wolverhampton WanderersWolves | 21 | 4 | 4 | 13 | 31 | 48 | -17 | 16 |
| 18 | Ipswich TownIpswich | 21 | 3 | 7 | 11 | 20 | 37 | -17 | 16 |
| 19 | Leicester CityLeicester | 22 | 3 | 5 | 14 | 23 | 48 | -25 | 14 |
| 20 | Southampton | 21 | 1 | 3 | 17 | 13 | 47 | -34 | 6 |
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