The 25-year-old was thought to be on Chelsea's radar midway through last season, while Swansea City were also interested in the Spaniard.
Reds boss Brendan Rodgers could make an offer of around £8.5m for the forward before the start of the new campaign, according to The Express.
Aspas has scored 11 goals in 32 games for Celta Vigo this season.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Liverpool | 17 | 13 | 3 | 1 | 40 | 17 | 23 | 42 |
| 2 | Nottingham ForestNott'm Forest | 19 | 11 | 4 | 4 | 26 | 19 | 7 | 37 |
| 3 | Arsenal | 18 | 10 | 6 | 2 | 35 | 16 | 19 | 36 |
| 4 | Chelsea | 18 | 10 | 5 | 3 | 38 | 21 | 17 | 35 |
| 5 | Manchester CityMan City | 19 | 9 | 4 | 6 | 32 | 26 | 6 | 31 |
| 6 | Newcastle UnitedNewcastle | 18 | 8 | 5 | 5 | 30 | 21 | 9 | 29 |
| 7 | Bournemouth | 18 | 8 | 5 | 5 | 27 | 21 | 6 | 29 |
| 8 | Fulham | 18 | 7 | 7 | 4 | 26 | 23 | 3 | 28 |
| 9 | Aston Villa | 18 | 8 | 4 | 6 | 26 | 29 | -3 | 28 |
| 10 | Brighton & Hove AlbionBrighton | 18 | 6 | 8 | 4 | 27 | 26 | 1 | 26 |
| 11 | Brentford | 18 | 7 | 3 | 8 | 32 | 32 | 0 | 24 |
| 12 | Tottenham HotspurSpurs | 18 | 7 | 2 | 9 | 39 | 26 | 13 | 23 |
| 13 | West Ham UnitedWest Ham | 18 | 6 | 5 | 7 | 23 | 30 | -7 | 23 |
| 14 | Manchester UnitedMan Utd | 18 | 6 | 4 | 8 | 21 | 24 | -3 | 22 |
| 15 | Crystal Palace | 19 | 4 | 8 | 7 | 20 | 27 | -7 | 20 |
| 16 | Everton | 18 | 3 | 8 | 7 | 15 | 24 | -9 | 17 |
| 17 | Wolverhampton WanderersWolves | 18 | 4 | 3 | 11 | 29 | 40 | -11 | 15 |
| 18 | Leicester CityLeicester | 19 | 3 | 5 | 11 | 22 | 42 | -20 | 14 |
| 19 | Ipswich TownIpswich | 18 | 2 | 6 | 10 | 16 | 33 | -17 | 12 |
| 20 | Southampton | 19 | 1 | 3 | 15 | 12 | 39 | -27 | 6 |
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