The 24-year-old striker, who joined the club from Liverpool for around £15m last month, is currently suffering from a heel injury.
"He's a few weeks away," Allardyce told Sky Sports News. "There's still a few weeks to go before he starts running."
Carroll scored seven goals for the Hammers during a loan spell at Upton Park last season.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Arsenal | 34 | 24 | 5 | 5 | 82 | 26 | 56 | 77 |
| 2 | Liverpool | 33 | 22 | 8 | 3 | 75 | 32 | 43 | 74 |
| 3 | Manchester CityMan City | 32 | 22 | 7 | 3 | 76 | 32 | 44 | 73 |
| 4 | Aston Villa | 34 | 20 | 6 | 8 | 71 | 50 | 21 | 66 |
| 5 | Tottenham HotspurSpurs | 32 | 18 | 6 | 8 | 65 | 49 | 16 | 60 |
| 6 | Newcastle UnitedNewcastle | 32 | 15 | 5 | 12 | 69 | 52 | 17 | 50 |
| 7 | Manchester UnitedMan Utd | 32 | 15 | 5 | 12 | 47 | 48 | -1 | 50 |
| 8 | West Ham UnitedWest Ham | 34 | 13 | 9 | 12 | 54 | 63 | -9 | 48 |
| 9 | Chelsea | 32 | 13 | 8 | 11 | 61 | 57 | 4 | 47 |
| 10 | Brighton & Hove AlbionBrighton | 32 | 11 | 11 | 10 | 52 | 50 | 2 | 44 |
| 11 | Wolverhampton WanderersWolves | 33 | 12 | 7 | 14 | 46 | 53 | -7 | 43 |
| 12 | Fulham | 34 | 12 | 6 | 16 | 50 | 54 | -4 | 42 |
| 13 | Bournemouth | 33 | 11 | 9 | 13 | 48 | 60 | -12 | 42 |
| 14 | Crystal Palace | 33 | 9 | 9 | 15 | 42 | 56 | -14 | 36 |
| 15 | Brentford | 34 | 9 | 8 | 17 | 52 | 59 | -7 | 35 |
| 16 | Everton | 33 | 10 | 8 | 15 | 34 | 48 | -14 | 30 |
| 17 | Nottingham ForestNott'm Forest | 34 | 7 | 9 | 18 | 42 | 60 | -18 | 26 |
| 18 | Luton TownLuton | 34 | 6 | 7 | 21 | 47 | 75 | -28 | 25 |
| 19 | Burnley | 34 | 5 | 8 | 21 | 37 | 69 | -32 | 23 |
| 20 | Sheffield UnitedSheff Utd | 33 | 3 | 7 | 23 | 31 | 88 | -57 | 16 |
| > Premier League Full Table | |||||||||
