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 | Ipswich TownIpswich | 43 | 26 | 11 | 6 | 85 | 53 | 32 | 89 |
| 2 | Leicester CityLeicester | 42 | 28 | 4 | 10 | 79 | 38 | 41 | 88 |
| 3 | Leeds UnitedLeeds | 43 | 26 | 9 | 8 | 76 | 34 | 42 | 87 |
| 4 | Southampton | 42 | 25 | 9 | 8 | 84 | 54 | 30 | 84 |
| 5 | West Bromwich AlbionWest Brom | 43 | 20 | 12 | 11 | 66 | 42 | 24 | 72 |
| 6 | Norwich CityNorwich | 43 | 21 | 8 | 14 | 76 | 60 | 16 | 71 |
| 7 | Hull City | 42 | 18 | 11 | 13 | 62 | 54 | 8 | 65 |
| 8 | Coventry CityCoventry | 42 | 17 | 12 | 13 | 66 | 52 | 14 | 63 |
| 9 | Middlesbrough | 43 | 18 | 9 | 16 | 61 | 56 | 5 | 63 |
| 10 | Preston North EndPreston | 43 | 18 | 9 | 16 | 56 | 60 | -4 | 63 |
| 11 | Cardiff CityCardiff | 43 | 18 | 5 | 20 | 48 | 60 | -12 | 59 |
| 12 | Bristol City | 43 | 16 | 10 | 17 | 50 | 46 | 4 | 58 |
| 13 | Sunderland | 43 | 16 | 8 | 19 | 52 | 50 | 2 | 56 |
| 14 | Swansea CitySwansea | 43 | 14 | 11 | 18 | 53 | 62 | -9 | 53 |
| 15 | Watford | 43 | 12 | 16 | 15 | 59 | 58 | 1 | 52 |
| 16 | Millwall | 43 | 13 | 11 | 19 | 42 | 55 | -13 | 50 |
| 17 | Blackburn RoversBlackburn | 43 | 13 | 10 | 20 | 57 | 71 | -14 | 49 |
| 18 | Plymouth ArgylePlymouth | 43 | 12 | 12 | 19 | 58 | 66 | -8 | 48 |
| 19 | Queens Park RangersQPR | 43 | 12 | 11 | 20 | 40 | 57 | -17 | 47 |
| 20 | Stoke CityStoke | 43 | 12 | 11 | 20 | 41 | 60 | -19 | 47 |
| 21 | Birmingham CityBirmingham | 43 | 12 | 9 | 22 | 48 | 64 | -16 | 45 |
| 22 | Huddersfield TownHuddersfield | 43 | 9 | 17 | 17 | 47 | 70 | -23 | 44 |
| 23 | Sheffield WednesdaySheff Weds | 43 | 12 | 8 | 23 | 36 | 67 | -31 | 44 |
| R | Rotherham UnitedRotherham | 43 | 4 | 11 | 28 | 32 | 85 | -53 | 23 |
| > Championship Full Table | |||||||||
