The 28-year-old is without a club after leaving the Trotters at the end of the Championship season.
Forest boss Dougie Freedman worked with Mills during his time in charge of Bolton.
Mills underwent a medical with the Reds on Saturday, with Freedman keen to snap him up ahead of interest from Fulham, according to the Daily Mail.
Mills made 94 appearances for Bolton during his three years with the club.
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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