The 28-year-old, who has also played for Blackpool, Leeds United and Ipswich Town, is a free agent following a stint in India with Mumbai City.
According to BBC Sport, the centre-back will undergo a medical at Dens Park today, with the move potentially being finalised tomorrow morning.
Dublin-born O'Dea has been capped by the Republic of Ireland on 20 occasions.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| Championship Group | |||||||||
| C | Celtic | 5 | 5 | 0 | 0 | 95 | 30 | 65 | 93 |
| 2 | RangersRangers | 5 | 3 | 1 | 1 | 87 | 32 | 55 | 85 |
| 3 | Hearts | 5 | 1 | 3 | 1 | 54 | 42 | 12 | 68 |
| 4 | Kilmarnock | 5 | 1 | 2 | 2 | 46 | 44 | 2 | 56 |
| 5 | St Mirren | 5 | 1 | 1 | 3 | 46 | 52 | -6 | 47 |
| 6 | Dundee | 5 | 0 | 1 | 4 | 49 | 68 | -19 | 42 |
| Relegation Group | |||||||||
| 1 | Aberdeen | 5 | 4 | 1 | 0 | 48 | 52 | -4 | 48 |
| 2 | Hibernian | 5 | 2 | 1 | 2 | 52 | 59 | -7 | 46 |
| 3 | Motherwell | 5 | 2 | 0 | 3 | 56 | 59 | -3 | 43 |
| 4 | St Johnstone | 5 | 1 | 1 | 3 | 29 | 54 | -25 | 35 |
| 5 | Ross County | 5 | 1 | 2 | 2 | 38 | 67 | -29 | 35 |
| R | Livingston | 5 | 2 | 1 | 2 | 29 | 70 | -41 | 25 |
| First Phase | |||||||||
| C | 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 |
| R | Livingston | 33 | 3 | 9 | 21 | 22 | 59 | -37 | 18 |
| > Scottish Premiership Full Table | |||||||||
