The 25-year-old Irishman, who joined the Dons from Wolverhampton Wanderers in 2009, is out of contract this summer.
While a number of clubs are thought to be monitoring Gleeson, Birmingham are confident of winning the race for his signature, according to Sky Sports News.
Gleeson scored three goals in 42 appearances for MK Dons during the 2013-14 campaign.
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 | |||||||||
