Hammers boss Slaven Bilic is looking to strengthen his squad after taking charge of the London outfit earlier this month.
The club have already signed Pedro Obiang since Bilic's appointment, and lead the race to sign Payet, according to Sky Sports News.
Payet, who has been capped by France, scored seven goals in 37 appearances for Marseille last season.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Liverpool | 23 | 17 | 5 | 1 | 56 | 21 | 35 | 56 |
| 2 | Arsenal | 24 | 14 | 8 | 2 | 49 | 22 | 27 | 50 |
| 3 | Nottingham ForestNott'm Forest | 24 | 14 | 5 | 5 | 40 | 27 | 13 | 47 |
| 4 | Manchester CityMan City | 24 | 12 | 5 | 7 | 48 | 35 | 13 | 41 |
| 5 | Newcastle UnitedNewcastle | 24 | 12 | 5 | 7 | 42 | 29 | 13 | 41 |
| 6 | Chelsea | 23 | 11 | 7 | 5 | 45 | 30 | 15 | 40 |
| 7 | Bournemouth | 24 | 11 | 7 | 6 | 41 | 28 | 13 | 40 |
| 8 | Aston Villa | 24 | 10 | 7 | 7 | 34 | 37 | -3 | 37 |
| 9 | Fulham | 24 | 9 | 9 | 6 | 36 | 32 | 4 | 36 |
| 10 | Brighton & Hove AlbionBrighton | 24 | 8 | 10 | 6 | 35 | 38 | -3 | 34 |
| 11 | Brentford | 24 | 9 | 4 | 11 | 42 | 42 | 0 | 31 |
| 12 | Crystal Palace | 24 | 7 | 9 | 8 | 28 | 30 | -2 | 30 |
| 13 | Manchester UnitedMan Utd | 24 | 8 | 5 | 11 | 28 | 34 | -6 | 29 |
| 14 | Tottenham HotspurSpurs | 24 | 8 | 3 | 13 | 48 | 37 | 11 | 27 |
| 15 | West Ham UnitedWest Ham | 23 | 7 | 6 | 10 | 28 | 44 | -16 | 27 |
| 16 | Everton | 23 | 6 | 8 | 9 | 23 | 28 | -5 | 26 |
| 17 | Wolverhampton WanderersWolves | 24 | 5 | 4 | 15 | 34 | 52 | -18 | 19 |
| 18 | Leicester CityLeicester | 24 | 4 | 5 | 15 | 25 | 53 | -28 | 17 |
| 19 | Ipswich TownIpswich | 24 | 3 | 7 | 14 | 22 | 49 | -27 | 16 |
| 20 | Southampton | 24 | 2 | 3 | 19 | 18 | 54 | -36 | 9 |
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