The 26-year-old is believed to have been the subject of offers below £900,000 from Forest, who are keen on securing his services before the window closes on Friday.
While Rangers are trying to cut costs at the club, they have told Forest that they will need to increase their bid for the player, according to BBC Sport.
Wallace's current contract at Ibrox expires in 2017.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| Championship Group | |||||||||
| 1 | Celtic | 0 | 0 | 0 | 0 | 80 | 26 | 54 | 78 |
| 2 | RangersRangers | 0 | 0 | 0 | 0 | 72 | 23 | 49 | 75 |
| 3 | Hearts | 0 | 0 | 0 | 0 | 46 | 34 | 12 | 62 |
| 4 | Kilmarnock | 0 | 0 | 0 | 0 | 43 | 34 | 9 | 51 |
| 5 | St Mirren | 0 | 0 | 0 | 0 | 38 | 43 | -5 | 43 |
| 6 | Dundee | 0 | 0 | 0 | 0 | 44 | 54 | -10 | 41 |
| Relegation Group | |||||||||
| 1 | Hibernian | 0 | 0 | 0 | 0 | 44 | 51 | -7 | 39 |
| 2 | Motherwell | 0 | 0 | 0 | 0 | 46 | 51 | -5 | 37 |
| 3 | Aberdeen | 0 | 0 | 0 | 0 | 35 | 49 | -14 | 35 |
| 4 | St Johnstone | 0 | 0 | 0 | 0 | 24 | 46 | -22 | 31 |
| 5 | Ross County | 0 | 0 | 0 | 0 | 32 | 56 | -24 | 30 |
| 6 | Livingston | 0 | 0 | 0 | 0 | 22 | 59 | -37 | 18 |
| First Phase | |||||||||
| 1 | Celtic | 33 | 24 | 6 | 3 | 80 | 26 | 54 | 78 |
| 2 | RangersRangers | 33 | 24 | 3 | 6 | 72 | 23 | 49 | 75 |
| 3 | Hearts | 33 | 19 | 5 | 9 | 46 | 34 | 12 | 62 |
| 4 | Kilmarnock | 33 | 13 | 12 | 8 | 43 | 34 | 9 | 51 |
| 5 | St Mirren | 33 | 12 | 7 | 14 | 38 | 43 | -5 | 43 |
| 6 | Dundee | 33 | 10 | 11 | 12 | 44 | 54 | -10 | 41 |
| 7 | Hibernian | 33 | 9 | 12 | 12 | 44 | 51 | -7 | 39 |
| 8 | Motherwell | 33 | 8 | 13 | 12 | 46 | 51 | -5 | 37 |
| 9 | Aberdeen | 33 | 8 | 11 | 14 | 35 | 49 | -14 | 35 |
| 10 | St Johnstone | 33 | 7 | 10 | 16 | 24 | 46 | -22 | 31 |
| 11 | Ross County | 33 | 7 | 9 | 17 | 32 | 56 | -24 | 30 |
| 12 | Livingston | 33 | 3 | 9 | 21 | 22 | 59 | -37 | 18 |
| > Scottish Premiership Full Table | |||||||||
