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 | |
| 1 | Liverpool | 18 | 14 | 3 | 1 | 45 | 17 | 28 | 45 |
| 2 | Arsenal | 19 | 11 | 6 | 2 | 38 | 17 | 21 | 39 |
| 3 | Nottingham ForestNott'm Forest | 19 | 11 | 4 | 4 | 26 | 19 | 7 | 37 |
| 4 | Chelsea | 19 | 10 | 5 | 4 | 38 | 23 | 15 | 35 |
| 5 | Newcastle UnitedNewcastle | 19 | 9 | 5 | 5 | 32 | 21 | 11 | 32 |
| 6 | Manchester CityMan City | 19 | 9 | 4 | 6 | 32 | 26 | 6 | 31 |
| 7 | Bournemouth | 19 | 8 | 6 | 5 | 29 | 23 | 6 | 30 |
| 8 | Fulham | 19 | 7 | 8 | 4 | 28 | 25 | 3 | 29 |
| 9 | Aston Villa | 19 | 8 | 5 | 6 | 28 | 31 | -3 | 29 |
| 10 | Brighton & Hove AlbionBrighton | 19 | 6 | 9 | 4 | 29 | 28 | 1 | 27 |
| 11 | Tottenham HotspurSpurs | 19 | 7 | 3 | 9 | 41 | 28 | 13 | 24 |
| 12 | Brentford | 19 | 7 | 3 | 9 | 33 | 35 | -2 | 24 |
| 13 | West Ham UnitedWest Ham | 19 | 6 | 5 | 8 | 23 | 35 | -12 | 23 |
| 14 | Manchester UnitedMan Utd | 19 | 6 | 4 | 9 | 21 | 26 | -5 | 22 |
| 15 | Crystal Palace | 19 | 4 | 8 | 7 | 20 | 27 | -7 | 20 |
| 16 | Everton | 18 | 3 | 8 | 7 | 15 | 24 | -9 | 17 |
| 17 | Wolverhampton WanderersWolves | 19 | 4 | 4 | 11 | 31 | 42 | -11 | 16 |
| 18 | Ipswich TownIpswich | 19 | 3 | 6 | 10 | 18 | 33 | -15 | 15 |
| 19 | Leicester CityLeicester | 19 | 3 | 5 | 11 | 22 | 42 | -20 | 14 |
| 20 | Southampton | 19 | 1 | 3 | 15 | 12 | 39 | -27 | 6 |
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