The former Southampton boss has already met with club officials to discuss a potential move to the Madejski Stadium, according to talkSPORT.
Adkins is not the only candidate for the Royals hot seat. Paolo Di Canio, Roberto Di Matteo and Gus Poyet have all been linked with the post.
The 45-year-old has not managed since the Saints replaced him with Mauricio Pocchetino in January.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Birmingham CityBirmingham | 8 | 7 | 1 | 0 | 17 | 8 | 9 | 22 |
| 2 | Wrexham | 9 | 5 | 2 | 2 | 14 | 7 | 7 | 17 |
| 3 | Mansfield TownMansfield | 8 | 5 | 2 | 1 | 15 | 11 | 4 | 17 |
| 4 | Stockport CountyStockport | 8 | 4 | 3 | 1 | 13 | 7 | 6 | 15 |
| 5 | Lincoln CityLincoln | 8 | 4 | 3 | 1 | 13 | 7 | 6 | 15 |
| 6 | Blackpool | 9 | 4 | 3 | 2 | 17 | 14 | 3 | 15 |
| 7 | Barnsley | 9 | 4 | 3 | 2 | 15 | 13 | 2 | 15 |
| 8 | Wycombe WanderersWycombe | 8 | 4 | 2 | 2 | 16 | 13 | 3 | 14 |
| 9 | Stevenage | 9 | 4 | 2 | 3 | 7 | 5 | 2 | 14 |
| 10 | Exeter CityExeter | 8 | 4 | 1 | 3 | 9 | 6 | 3 | 13 |
| 11 | Bolton WanderersBolton | 8 | 4 | 1 | 3 | 13 | 13 | 0 | 13 |
| 12 | Reading | 8 | 4 | 1 | 3 | 12 | 12 | 0 | 13 |
| 13 | Charlton AthleticCharlton | 9 | 4 | 1 | 4 | 9 | 9 | 0 | 13 |
| 14 | Wigan AthleticWigan | 9 | 3 | 3 | 3 | 9 | 5 | 4 | 12 |
| 15 | Huddersfield TownHuddersfield | 9 | 4 | 0 | 5 | 12 | 11 | 1 | 12 |
| 16 | Peterborough UnitedPeterborough | 9 | 3 | 2 | 4 | 14 | 17 | -3 | 11 |
| 17 | Rotherham UnitedRotherham | 9 | 2 | 4 | 3 | 7 | 10 | -3 | 10 |
| 18 | Bristol Rovers | 9 | 3 | 1 | 5 | 10 | 15 | -5 | 10 |
| 19 | Northampton TownNorthampton | 8 | 2 | 2 | 4 | 10 | 13 | -3 | 8 |
| 20 | Leyton Orient | 9 | 2 | 2 | 5 | 9 | 12 | -3 | 8 |
| 21 | Crawley TownCrawley | 8 | 2 | 1 | 5 | 5 | 12 | -7 | 7 |
| 22 | Burton Albion | 8 | 0 | 4 | 4 | 9 | 16 | -7 | 4 |
| 23 | Shrewsbury TownShrewsbury | 9 | 1 | 1 | 7 | 6 | 15 | -9 | 4 |
| 24 | Cambridge UnitedCambridge | 8 | 0 | 1 | 7 | 6 | 16 | -10 | 1 |
| > League One Full Table | |||||||||
