The 33-year-old midfielder, who has been training with the West London side, has been without a club since his release by Chelsea in the summer.
European clubs Reims and Malaga are said to have expressed an interest in signing the Israeli, but he is now ready to sign with Rangers.
According to BBC Sport, Leicester City, a promotion rival of QPR's this season, also made a late approach for Benayoun.
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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