The Ghanaian has been a key figure in the Robins' lineup following his £150,000 move from Barnet two years ago.
According to The Mirror, Swans boss Michael Laudrup is keen on adding the 24-year-old to his squad ahead of the new Premier League season.
Adomah, who made his international debut against Brazil at Craven Cottage last year, has scored 10 goals in 91 appearances for Bristol City.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Sunderland | 14 | 9 | 3 | 2 | 23 | 9 | 14 | 30 |
| 2 | Sheffield UnitedSheff Utd | 14 | 9 | 3 | 2 | 18 | 7 | 11 | 28 |
| 3 | Leeds UnitedLeeds | 14 | 7 | 5 | 2 | 22 | 9 | 13 | 26 |
| 4 | Burnley | 14 | 6 | 6 | 2 | 17 | 6 | 11 | 24 |
| 5 | West Bromwich AlbionWest Brom | 14 | 5 | 7 | 2 | 14 | 8 | 6 | 22 |
| 6 | Millwall | 14 | 6 | 4 | 4 | 17 | 12 | 5 | 22 |
| 7 | Watford | 14 | 7 | 1 | 6 | 22 | 22 | 0 | 22 |
| 8 | Middlesbrough | 14 | 6 | 3 | 5 | 18 | 16 | 2 | 21 |
| 9 | Swansea CitySwansea | 14 | 5 | 4 | 5 | 11 | 9 | 2 | 19 |
| 10 | Blackburn RoversBlackburn | 14 | 5 | 4 | 5 | 16 | 16 | 0 | 19 |
| 11 | Bristol City | 14 | 4 | 7 | 3 | 18 | 19 | -1 | 19 |
| 12 | Norwich CityNorwich | 14 | 4 | 6 | 4 | 23 | 20 | 3 | 18 |
| 13 | Derby CountyDerby | 14 | 5 | 3 | 6 | 18 | 18 | 0 | 18 |
| 14 | Stoke CityStoke | 14 | 5 | 3 | 6 | 17 | 18 | -1 | 18 |
| 15 | Sheffield WednesdaySheff Weds | 14 | 5 | 3 | 6 | 17 | 24 | -7 | 18 |
| 16 | Oxford UnitedOxford Utd | 14 | 4 | 5 | 5 | 17 | 17 | 0 | 17 |
| 17 | Coventry CityCoventry | 14 | 4 | 3 | 7 | 18 | 19 | -1 | 15 |
| 18 | Hull City | 14 | 3 | 6 | 5 | 15 | 18 | -3 | 15 |
| 19 | Luton TownLuton | 14 | 4 | 3 | 7 | 16 | 21 | -5 | 15 |
| 20 | Preston North EndPreston | 14 | 3 | 6 | 5 | 14 | 20 | -6 | 15 |
| 21 | Cardiff CityCardiff | 14 | 4 | 3 | 7 | 13 | 20 | -7 | 15 |
| 22 | Plymouth ArgylePlymouth | 14 | 4 | 3 | 7 | 14 | 25 | -11 | 15 |
| 23 | Queens Park RangersQPR | 14 | 1 | 7 | 6 | 12 | 23 | -11 | 10 |
| 24 | Portsmouth | 14 | 1 | 6 | 7 | 13 | 27 | -14 | 9 |
| > Championship Full Table | |||||||||
