The 24-year-old was recently placed on the transfer list at Broadhall Way, with the club having claimed that he had failed to settle under manager Graham Westley.
That has alerted Scottish Premiership side St Johnstone, who have had an offer for the former Arsenal trainee accepted, according to Sky Sports News.
Dunne was voted Stevenage's Player of the Season last term.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Wycombe WanderersWycombe | 14 | 10 | 2 | 2 | 32 | 16 | 16 | 32 |
| 2 | Birmingham CityBirmingham | 13 | 9 | 3 | 1 | 24 | 12 | 12 | 30 |
| 3 | Wrexham | 15 | 8 | 4 | 3 | 22 | 11 | 11 | 28 |
| 4 | Stockport CountyStockport | 16 | 7 | 6 | 3 | 26 | 17 | 9 | 27 |
| 5 | Barnsley | 15 | 7 | 5 | 3 | 24 | 19 | 5 | 26 |
| 6 | Lincoln CityLincoln | 15 | 7 | 5 | 3 | 21 | 17 | 4 | 26 |
| 7 | Mansfield TownMansfield | 13 | 7 | 3 | 3 | 20 | 15 | 5 | 24 |
| 8 | Huddersfield TownHuddersfield | 14 | 7 | 2 | 5 | 21 | 14 | 7 | 23 |
| 9 | Exeter CityExeter | 14 | 7 | 2 | 5 | 14 | 10 | 4 | 23 |
| 10 | Reading | 14 | 7 | 2 | 5 | 22 | 21 | 1 | 23 |
| 11 | Bolton WanderersBolton | 14 | 7 | 2 | 5 | 22 | 24 | -2 | 23 |
| 12 | Peterborough UnitedPeterborough | 15 | 6 | 3 | 6 | 31 | 27 | 4 | 21 |
| 13 | Charlton AthleticCharlton | 14 | 5 | 4 | 5 | 15 | 15 | 0 | 19 |
| 14 | Bristol Rovers | 15 | 5 | 3 | 7 | 16 | 21 | -5 | 18 |
| 15 | Stevenage | 15 | 5 | 3 | 7 | 11 | 16 | -5 | 18 |
| 16 | Northampton TownNorthampton | 15 | 4 | 5 | 6 | 18 | 21 | -3 | 17 |
| 17 | Rotherham UnitedRotherham | 15 | 4 | 5 | 6 | 14 | 18 | -4 | 17 |
| 18 | Blackpool | 15 | 4 | 5 | 6 | 21 | 28 | -7 | 17 |
| 19 | Wigan AthleticWigan | 14 | 3 | 5 | 6 | 12 | 12 | 0 | 14 |
| 20 | Leyton Orient | 14 | 4 | 2 | 8 | 14 | 18 | -4 | 14 |
| 21 | Crawley TownCrawley | 16 | 3 | 4 | 9 | 14 | 27 | -13 | 13 |
| 22 | Cambridge UnitedCambridge | 14 | 3 | 2 | 9 | 13 | 24 | -11 | 11 |
| 23 | Burton Albion | 14 | 1 | 5 | 8 | 15 | 25 | -10 | 8 |
| 24 | Shrewsbury TownShrewsbury | 15 | 2 | 2 | 11 | 13 | 27 | -14 | 8 |
| > League One Full Table | |||||||||
