The newly-promoted Clarets are believed to have submitted a bid in the region of £1m for the 24-year-old over the weekend.
However, the West Brom board rebuffed that approach and have informed their Premier League counterparts that they would not welcome a second offer, according to the Express & Star.
Dawson, who joined the Baggies in 2010, made 15 appearances in all competitions last season.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Leeds UnitedLeeds | 16 | 9 | 5 | 2 | 28 | 12 | 16 | 32 |
| 2 | Sunderland | 16 | 9 | 5 | 2 | 26 | 12 | 14 | 32 |
| 3 | Sheffield UnitedSheff Utd | 16 | 10 | 4 | 2 | 21 | 9 | 12 | 32 |
| 4 | Burnley | 16 | 8 | 6 | 2 | 19 | 6 | 13 | 30 |
| 5 | Middlesbrough | 16 | 8 | 3 | 5 | 29 | 19 | 10 | 27 |
| 6 | West Bromwich AlbionWest Brom | 16 | 6 | 8 | 2 | 18 | 11 | 7 | 26 |
| 7 | Watford | 16 | 8 | 2 | 6 | 25 | 24 | 1 | 26 |
| 8 | Millwall | 16 | 6 | 6 | 4 | 19 | 14 | 5 | 24 |
| 9 | Blackburn RoversBlackburn | 15 | 6 | 4 | 5 | 19 | 17 | 2 | 22 |
| 10 | Bristol City | 16 | 5 | 7 | 4 | 20 | 20 | 0 | 22 |
| 11 | Derby CountyDerby | 16 | 5 | 5 | 6 | 20 | 20 | 0 | 20 |
| 12 | Stoke CityStoke | 16 | 5 | 5 | 6 | 19 | 20 | -1 | 20 |
| 13 | Norwich CityNorwich | 16 | 4 | 7 | 5 | 25 | 24 | 1 | 19 |
| 14 | Swansea CitySwansea | 16 | 5 | 4 | 7 | 14 | 14 | 0 | 19 |
| 15 | Sheffield WednesdaySheff Weds | 16 | 5 | 4 | 7 | 18 | 26 | -8 | 19 |
| 16 | Luton TownLuton | 16 | 5 | 3 | 8 | 18 | 26 | -8 | 18 |
| 17 | Coventry CityCoventry | 16 | 4 | 5 | 7 | 22 | 23 | -1 | 17 |
| 18 | Oxford UnitedOxford Utd | 16 | 4 | 5 | 7 | 19 | 24 | -5 | 17 |
| 19 | Plymouth ArgylePlymouth | 16 | 4 | 5 | 7 | 17 | 28 | -11 | 17 |
| 20 | Preston North EndPreston | 16 | 3 | 7 | 6 | 16 | 24 | -8 | 16 |
| 21 | Cardiff CityCardiff | 16 | 4 | 4 | 8 | 15 | 24 | -9 | 16 |
| 22 | Hull City | 16 | 3 | 6 | 7 | 16 | 21 | -5 | 15 |
| 23 | Portsmouth | 15 | 2 | 6 | 7 | 16 | 28 | -12 | 12 |
| 24 | Queens Park RangersQPR | 16 | 1 | 8 | 7 | 13 | 26 | -13 | 11 |
| > Championship Full Table | |||||||||
