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 | 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 | |||||||||
