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 | |
| C | Portsmouth | 44 | 27 | 13 | 4 | 75 | 39 | 36 | 94 |
| 2 | Derby CountyDerby | 44 | 26 | 8 | 10 | 75 | 37 | 38 | 86 |
| 3 | Bolton WanderersBolton | 44 | 24 | 11 | 9 | 81 | 48 | 33 | 83 |
| 4 | Peterborough UnitedPeterborough | 43 | 24 | 8 | 11 | 84 | 56 | 28 | 80 |
| 5 | Barnsley | 44 | 21 | 12 | 11 | 79 | 60 | 19 | 75 |
| 6 | Oxford UnitedOxford Utd | 44 | 21 | 10 | 13 | 76 | 54 | 22 | 73 |
| 7 | Lincoln CityLincoln | 44 | 19 | 14 | 11 | 63 | 37 | 26 | 71 |
| 8 | Blackpool | 44 | 20 | 10 | 14 | 60 | 43 | 17 | 70 |
| 9 | Stevenage | 44 | 18 | 13 | 13 | 54 | 44 | 10 | 67 |
| 10 | Leyton Orient | 44 | 17 | 11 | 16 | 50 | 53 | -3 | 62 |
| 11 | Northampton TownNorthampton | 44 | 17 | 8 | 19 | 55 | 63 | -8 | 59 |
| 12 | Wycombe WanderersWycombe | 43 | 15 | 13 | 15 | 55 | 53 | 2 | 58 |
| 13 | Exeter CityExeter | 44 | 16 | 10 | 18 | 43 | 58 | -15 | 58 |
| 14 | Bristol Rovers | 44 | 16 | 9 | 19 | 52 | 64 | -12 | 57 |
| 15 | Wigan AthleticWigan | 44 | 18 | 10 | 16 | 59 | 55 | 4 | 56 |
| 16 | Charlton AthleticCharlton | 44 | 11 | 19 | 14 | 63 | 63 | 0 | 52 |
| 17 | Reading | 44 | 15 | 11 | 18 | 63 | 65 | -2 | 50 |
| 18 | Shrewsbury TownShrewsbury | 44 | 13 | 8 | 23 | 33 | 63 | -30 | 47 |
| 19 | Cambridge UnitedCambridge | 43 | 12 | 10 | 21 | 38 | 59 | -21 | 46 |
| 20 | Burton Albion | 44 | 11 | 10 | 23 | 36 | 62 | -26 | 43 |
| 21 | Cheltenham TownCheltenham | 43 | 11 | 8 | 24 | 37 | 61 | -24 | 41 |
| 22 | Port Vale | 44 | 10 | 10 | 24 | 41 | 72 | -31 | 40 |
| 23 | Fleetwood TownFleetwood | 44 | 8 | 13 | 23 | 45 | 72 | -27 | 37 |
| R | Carlisle UnitedCarlisle | 44 | 7 | 9 | 28 | 40 | 76 | -36 | 30 |
| > League One Full Table | |||||||||
