Dempsey, 29, scored 23 goals in all competitions last season and has 12 months remaining on his current contract.
Liverpool are understood to be tracking the American, and the Cottagers intend to use that interest to help them strike a deal for Carroll, according to The Mirror.
Fulham paid £1.5m for Dempsey when he arrived from New England Revolution in 2007.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Arsenal | 36 | 26 | 5 | 5 | 88 | 28 | 60 | 83 |
| 2 | Manchester CityMan City | 35 | 25 | 7 | 3 | 87 | 33 | 54 | 82 |
| 3 | Liverpool | 36 | 23 | 9 | 4 | 81 | 38 | 43 | 78 |
| 4 | Aston Villa | 36 | 20 | 7 | 9 | 73 | 53 | 20 | 67 |
| 5 | Tottenham HotspurSpurs | 35 | 18 | 6 | 11 | 69 | 58 | 11 | 60 |
| 6 | Newcastle UnitedNewcastle | 35 | 17 | 5 | 13 | 78 | 56 | 22 | 56 |
| 7 | Chelsea | 35 | 15 | 9 | 11 | 70 | 59 | 11 | 54 |
| 8 | Manchester UnitedMan Utd | 34 | 16 | 6 | 12 | 52 | 51 | 1 | 54 |
| 9 | West Ham UnitedWest Ham | 36 | 13 | 10 | 13 | 56 | 70 | -14 | 49 |
| 10 | Bournemouth | 36 | 13 | 9 | 14 | 52 | 63 | -11 | 48 |
| 11 | Brighton & Hove AlbionBrighton | 35 | 12 | 11 | 12 | 53 | 57 | -4 | 47 |
| 12 | Wolverhampton WanderersWolves | 36 | 13 | 7 | 16 | 49 | 60 | -11 | 46 |
| 13 | Fulham | 36 | 12 | 8 | 16 | 51 | 55 | -4 | 44 |
| 14 | Crystal Palace | 35 | 10 | 10 | 15 | 45 | 57 | -12 | 40 |
| 15 | Everton | 36 | 12 | 9 | 15 | 38 | 49 | -11 | 37 |
| 16 | Brentford | 36 | 9 | 9 | 18 | 52 | 60 | -8 | 36 |
| 17 | Nottingham ForestNott'm Forest | 36 | 8 | 9 | 19 | 45 | 63 | -18 | 29 |
| 18 | Luton TownLuton | 36 | 6 | 8 | 22 | 49 | 78 | -29 | 26 |
| 19 | Burnley | 36 | 5 | 9 | 22 | 39 | 74 | -35 | 24 |
| R | Sheffield UnitedSheff Utd | 36 | 3 | 7 | 26 | 35 | 100 | -65 | 16 |
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