The Gunners are said to be keen on the 22-year-old, with manager Arsene Wenger recently likening the player to Samir Nasri.
However, Reds boss Brendan Rodgers is also interested in the OL playmaker, and will offer a bid of £12.8m for the player, according to L'Equipe.
Grenier is said to have a €37m (£31m) buy-out clause inserted into his contract with Lyon.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| C | Manchester CityMan City | 38 | 28 | 7 | 3 | 96 | 34 | 62 | 91 |
| 2 | Arsenal | 38 | 28 | 5 | 5 | 91 | 29 | 62 | 89 |
| 3 | Liverpool | 38 | 24 | 10 | 4 | 86 | 41 | 45 | 82 |
| 4 | Aston Villa | 38 | 20 | 8 | 10 | 76 | 61 | 15 | 68 |
| 5 | Tottenham HotspurSpurs | 38 | 20 | 6 | 12 | 74 | 61 | 13 | 66 |
| 6 | Chelsea | 38 | 18 | 9 | 11 | 77 | 63 | 14 | 63 |
| 7 | Newcastle UnitedNewcastle | 38 | 18 | 6 | 14 | 85 | 62 | 23 | 60 |
| 8 | Manchester UnitedMan Utd | 38 | 18 | 6 | 14 | 57 | 58 | -1 | 60 |
| 9 | West Ham UnitedWest Ham | 38 | 14 | 10 | 14 | 60 | 74 | -14 | 52 |
| 10 | Crystal Palace | 38 | 13 | 10 | 15 | 57 | 58 | -1 | 49 |
| 11 | Brighton & Hove AlbionBrighton | 38 | 12 | 12 | 14 | 55 | 62 | -7 | 48 |
| 12 | Bournemouth | 38 | 13 | 9 | 16 | 54 | 67 | -13 | 48 |
| 13 | Fulham | 38 | 13 | 8 | 17 | 55 | 61 | -6 | 47 |
| 14 | Wolverhampton WanderersWolves | 38 | 13 | 7 | 18 | 50 | 65 | -15 | 46 |
| 15 | Everton | 38 | 13 | 9 | 16 | 40 | 51 | -11 | 40 |
| 16 | Brentford | 38 | 10 | 9 | 19 | 56 | 65 | -9 | 39 |
| 17 | Nottingham ForestNott'm Forest | 38 | 9 | 9 | 20 | 49 | 67 | -18 | 32 |
| R | Luton TownLuton | 38 | 6 | 8 | 24 | 52 | 85 | -33 | 26 |
| R | Burnley | 38 | 5 | 9 | 24 | 41 | 78 | -37 | 24 |
| R | Sheffield UnitedSheff Utd | 38 | 3 | 7 | 28 | 35 | 104 | -69 | 16 |
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