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 | 7 | 6 | 0 | 1 | 13 | 2 | 11 | 18 |
| 2 | Manchester CityMan City | 7 | 5 | 2 | 0 | 17 | 8 | 9 | 17 |
| 3 | Arsenal | 7 | 5 | 2 | 0 | 15 | 6 | 9 | 17 |
| 4 | Chelsea | 7 | 4 | 2 | 1 | 16 | 8 | 8 | 14 |
| 5 | Aston Villa | 7 | 4 | 2 | 1 | 12 | 9 | 3 | 14 |
| 6 | Brighton & Hove AlbionBrighton | 7 | 3 | 3 | 1 | 13 | 10 | 3 | 12 |
| 7 | Newcastle UnitedNewcastle | 7 | 3 | 3 | 1 | 8 | 7 | 1 | 12 |
| 8 | Fulham | 7 | 3 | 2 | 2 | 10 | 8 | 2 | 11 |
| 9 | Tottenham HotspurSpurs | 7 | 3 | 1 | 3 | 14 | 8 | 6 | 10 |
| 10 | Nottingham ForestNott'm Forest | 7 | 2 | 4 | 1 | 7 | 6 | 1 | 10 |
| 11 | Brentford | 7 | 3 | 1 | 3 | 13 | 13 | 0 | 10 |
| 12 | West Ham UnitedWest Ham | 7 | 2 | 2 | 3 | 10 | 11 | -1 | 8 |
| 13 | Bournemouth | 7 | 2 | 2 | 3 | 8 | 10 | -2 | 8 |
| 14 | Manchester UnitedMan Utd | 7 | 2 | 2 | 3 | 5 | 8 | -3 | 8 |
| 15 | Leicester CityLeicester | 7 | 1 | 3 | 3 | 9 | 12 | -3 | 6 |
| 16 | Everton | 7 | 1 | 2 | 4 | 7 | 15 | -8 | 5 |
| 17 | Ipswich TownIpswich | 7 | 0 | 4 | 3 | 6 | 14 | -8 | 4 |
| 18 | Crystal Palace | 7 | 0 | 3 | 4 | 5 | 10 | -5 | 3 |
| 19 | Southampton | 7 | 0 | 1 | 6 | 4 | 15 | -11 | 1 |
| 20 | Wolverhampton WanderersWolves | 7 | 0 | 1 | 6 | 9 | 21 | -12 | 1 |
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