The 58-year-old's current deal with the Premier League outfit runs out at the end of the season.
"When it is all tied up, we want to put pen to paper and then we can move on with next season," he told BBC Sport.
"I will have a chat with the owners and hopefully by the end of the week I would have secured our future."
Allardyce has been at West Ham since 2011.
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 | 11 | 7 | 2 | 2 | 22 | 13 | 9 | 23 |
| 3 | Chelsea | 11 | 5 | 4 | 2 | 21 | 13 | 8 | 19 |
| 4 | Arsenal | 11 | 5 | 4 | 2 | 18 | 12 | 6 | 19 |
| 5 | Nottingham ForestNott'm Forest | 11 | 5 | 4 | 2 | 15 | 10 | 5 | 19 |
| 6 | Brighton & Hove AlbionBrighton | 11 | 5 | 4 | 2 | 19 | 15 | 4 | 19 |
| 7 | Fulham | 11 | 5 | 3 | 3 | 16 | 13 | 3 | 18 |
| 8 | Newcastle UnitedNewcastle | 11 | 5 | 3 | 3 | 13 | 11 | 2 | 18 |
| 9 | Aston Villa | 11 | 5 | 3 | 3 | 17 | 17 | 0 | 18 |
| 10 | Tottenham HotspurSpurs | 11 | 5 | 1 | 5 | 23 | 13 | 10 | 16 |
| 11 | Brentford | 11 | 5 | 1 | 5 | 22 | 22 | 0 | 16 |
| 12 | Bournemouth | 11 | 4 | 3 | 4 | 15 | 15 | 0 | 15 |
| 13 | Manchester UnitedMan Utd | 11 | 4 | 3 | 4 | 12 | 12 | 0 | 15 |
| 14 | West Ham UnitedWest Ham | 11 | 3 | 3 | 5 | 13 | 19 | -6 | 12 |
| 15 | Leicester CityLeicester | 11 | 2 | 4 | 5 | 14 | 21 | -7 | 10 |
| 16 | Everton | 11 | 2 | 4 | 5 | 10 | 17 | -7 | 10 |
| 17 | Ipswich TownIpswich | 11 | 1 | 5 | 5 | 12 | 22 | -10 | 8 |
| 18 | Crystal Palace | 11 | 1 | 4 | 6 | 8 | 15 | -7 | 7 |
| 19 | Wolverhampton WanderersWolves | 11 | 1 | 3 | 7 | 16 | 27 | -11 | 6 |
| 20 | Southampton | 11 | 1 | 1 | 9 | 7 | 21 | -14 | 4 |
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