It is understood that Anfield boss Brendan Rodgers will meet Fulham's asking price of £7.5m for the American, as he readies his squad for next season.
According to The Mirror, the deal could be tied up as soon as Wednesday so the attacker can join the Reds on their pre-season tour of the United States.
Dempsey scored 23 goals for Fulham last season.
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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