It is believed that the Clarets had a £2.5m bid for the 23-year-old rejected by their West London counterparts earlier this month.
However, according to Sky Sports News, the Turf Moor outfit will make an enhanced proposal in the near future.
The report adds that the Bees may be tempted to do business for around £5m.
Tarkowski joined his current employers from Oldham Athletic two years ago.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Sunderland | 15 | 9 | 4 | 2 | 25 | 11 | 14 | 31 |
| 2 | Sheffield UnitedSheff Utd | 15 | 10 | 3 | 2 | 19 | 7 | 12 | 31 |
| 3 | Leeds UnitedLeeds | 15 | 8 | 5 | 2 | 24 | 9 | 15 | 29 |
| 4 | Burnley | 15 | 7 | 6 | 2 | 18 | 6 | 12 | 27 |
| 5 | West Bromwich AlbionWest Brom | 15 | 6 | 7 | 2 | 16 | 9 | 7 | 25 |
| 6 | Watford | 15 | 8 | 1 | 6 | 23 | 22 | 1 | 25 |
| 7 | Middlesbrough | 15 | 7 | 3 | 5 | 23 | 17 | 6 | 24 |
| 8 | Millwall | 15 | 6 | 5 | 4 | 18 | 13 | 5 | 23 |
| 9 | Blackburn RoversBlackburn | 15 | 6 | 4 | 5 | 19 | 17 | 2 | 22 |
| 10 | Bristol City | 15 | 5 | 7 | 3 | 20 | 19 | 1 | 22 |
| 11 | Swansea CitySwansea | 15 | 5 | 4 | 6 | 11 | 10 | 1 | 19 |
| 12 | Derby CountyDerby | 15 | 5 | 4 | 6 | 19 | 19 | 0 | 19 |
| 13 | Stoke CityStoke | 15 | 5 | 4 | 6 | 18 | 19 | -1 | 19 |
| 14 | Norwich CityNorwich | 15 | 4 | 6 | 5 | 23 | 22 | 1 | 18 |
| 15 | Sheffield WednesdaySheff Weds | 15 | 5 | 3 | 7 | 17 | 25 | -8 | 18 |
| 16 | Oxford UnitedOxford Utd | 15 | 4 | 5 | 6 | 17 | 18 | -1 | 17 |
| 17 | Coventry CityCoventry | 15 | 4 | 4 | 7 | 20 | 21 | -1 | 16 |
| 18 | Plymouth ArgylePlymouth | 15 | 4 | 4 | 7 | 15 | 26 | -11 | 16 |
| 19 | Hull City | 15 | 3 | 6 | 6 | 16 | 20 | -4 | 15 |
| 20 | Preston North EndPreston | 15 | 3 | 6 | 6 | 15 | 23 | -8 | 15 |
| 21 | Luton TownLuton | 15 | 4 | 3 | 8 | 17 | 26 | -9 | 15 |
| 22 | Cardiff CityCardiff | 15 | 4 | 3 | 8 | 14 | 23 | -9 | 15 |
| 23 | Portsmouth | 15 | 2 | 6 | 7 | 16 | 28 | -12 | 12 |
| 24 | Queens Park RangersQPR | 15 | 1 | 7 | 7 | 12 | 25 | -13 | 10 |
| > Championship Full Table | |||||||||
