Andy Carroll arrived at the Hammers from Liverpool last month, but Carlton Cole, Marouane Chamakh and Wellington have all departed Upton Park this summer.
"We need goal scorers not defenders," Sullivan tweeted when asked about defensive transfer targets.
It has been reported that an ankle injury could see Carroll miss the start of the new season.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Arsenal | 37 | 27 | 5 | 5 | 89 | 28 | 61 | 86 |
| 2 | Manchester CityMan City | 36 | 26 | 7 | 3 | 91 | 33 | 58 | 85 |
| 3 | Liverpool | 37 | 23 | 10 | 4 | 84 | 41 | 43 | 79 |
| 4 | Aston Villa | 37 | 20 | 8 | 9 | 76 | 56 | 20 | 68 |
| 5 | Tottenham HotspurSpurs | 36 | 19 | 6 | 11 | 71 | 59 | 12 | 63 |
| 6 | Newcastle UnitedNewcastle | 36 | 17 | 6 | 13 | 79 | 57 | 22 | 57 |
| 7 | Chelsea | 36 | 16 | 9 | 11 | 73 | 61 | 12 | 57 |
| 8 | Manchester UnitedMan Utd | 36 | 16 | 6 | 14 | 52 | 56 | -4 | 54 |
| 9 | West Ham UnitedWest Ham | 37 | 14 | 10 | 13 | 59 | 71 | -12 | 52 |
| 10 | Brighton & Hove AlbionBrighton | 36 | 12 | 12 | 12 | 54 | 58 | -4 | 48 |
| 11 | Bournemouth | 37 | 13 | 9 | 15 | 53 | 65 | -12 | 48 |
| 12 | Crystal Palace | 37 | 12 | 10 | 15 | 52 | 58 | -6 | 46 |
| 13 | Wolverhampton WanderersWolves | 37 | 13 | 7 | 17 | 50 | 63 | -13 | 46 |
| 14 | Fulham | 37 | 12 | 8 | 17 | 51 | 59 | -8 | 44 |
| 15 | Everton | 37 | 13 | 9 | 15 | 39 | 49 | -10 | 40 |
| 16 | Brentford | 37 | 10 | 9 | 18 | 54 | 61 | -7 | 39 |
| 17 | Nottingham ForestNott'm Forest | 37 | 8 | 9 | 20 | 47 | 66 | -19 | 29 |
| 18 | Luton TownLuton | 37 | 6 | 8 | 23 | 50 | 81 | -31 | 26 |
| R | Burnley | 37 | 5 | 9 | 23 | 40 | 76 | -36 | 24 |
| R | Sheffield UnitedSheff Utd | 37 | 3 | 7 | 27 | 35 | 101 | -66 | 16 |
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