The 37-year-old former England captain is currently without a club following his recent departure from Los Angeles Galaxy.
When asked about the possible arrival of Beckham, Allardyce told reporters: "We will wait and see. You never know."
Beckham was at Upton Park on Saturday to watch West Ham draw 2-2 with former club Manchester United in the third round of the FA Cup.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Liverpool | 11 | 9 | 1 | 1 | 21 | 6 | 15 | 28 |
| 2 | Manchester CityMan City | 12 | 7 | 2 | 3 | 22 | 17 | 5 | 23 |
| 3 | Chelsea | 12 | 6 | 4 | 2 | 23 | 14 | 9 | 22 |
| 4 | Arsenal | 12 | 6 | 4 | 2 | 21 | 12 | 9 | 22 |
| 5 | Brighton & Hove AlbionBrighton | 12 | 6 | 4 | 2 | 21 | 16 | 5 | 22 |
| 6 | Tottenham HotspurSpurs | 12 | 6 | 1 | 5 | 27 | 13 | 14 | 19 |
| 7 | Nottingham ForestNott'm Forest | 12 | 5 | 4 | 3 | 15 | 13 | 2 | 19 |
| 8 | Aston Villa | 12 | 5 | 4 | 3 | 19 | 19 | 0 | 19 |
| 9 | Newcastle UnitedNewcastle | 11 | 5 | 3 | 3 | 13 | 11 | 2 | 18 |
| 10 | Fulham | 12 | 5 | 3 | 4 | 17 | 17 | 0 | 18 |
| 11 | Brentford | 12 | 5 | 2 | 5 | 22 | 22 | 0 | 17 |
| 12 | Manchester UnitedMan Utd | 11 | 4 | 3 | 4 | 12 | 12 | 0 | 15 |
| 13 | Bournemouth | 12 | 4 | 3 | 5 | 16 | 17 | -1 | 15 |
| 14 | West Ham UnitedWest Ham | 11 | 3 | 3 | 5 | 13 | 19 | -6 | 12 |
| 15 | Everton | 12 | 2 | 5 | 5 | 10 | 17 | -7 | 11 |
| 16 | Leicester CityLeicester | 12 | 2 | 4 | 6 | 15 | 23 | -8 | 10 |
| 17 | Wolverhampton WanderersWolves | 12 | 2 | 3 | 7 | 20 | 28 | -8 | 9 |
| 18 | Crystal Palace | 12 | 1 | 5 | 6 | 10 | 17 | -7 | 8 |
| 19 | Ipswich TownIpswich | 11 | 1 | 5 | 5 | 12 | 22 | -10 | 8 |
| 20 | Southampton | 11 | 1 | 1 | 9 | 7 | 21 | -14 | 4 |
| > Premier League Full Table | |||||||||
