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 | 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 | |||||||||
