The Merseysiders are thought to have recently turned down two bids from Premier League champions Manchester City for Agger.
Manager Brendan Rodgers has now turned his attention to the Uruguayan as a possible replacement, according to The Metro.
Godin joined Atletico from Villarreal in 2010 for around £6m.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Liverpool | 15 | 11 | 3 | 1 | 31 | 13 | 18 | 36 |
| 2 | Chelsea | 16 | 10 | 4 | 2 | 37 | 19 | 18 | 34 |
| 3 | Arsenal | 16 | 8 | 6 | 2 | 29 | 15 | 14 | 30 |
| 4 | Nottingham ForestNott'm Forest | 16 | 8 | 4 | 4 | 21 | 19 | 2 | 28 |
| 5 | Manchester CityMan City | 16 | 8 | 3 | 5 | 28 | 23 | 5 | 27 |
| 6 | Bournemouth | 16 | 7 | 4 | 5 | 24 | 21 | 3 | 25 |
| 7 | Aston Villa | 16 | 7 | 4 | 5 | 24 | 25 | -1 | 25 |
| 8 | Fulham | 16 | 6 | 6 | 4 | 24 | 22 | 2 | 24 |
| 9 | Brighton & Hove AlbionBrighton | 16 | 6 | 6 | 4 | 26 | 25 | 1 | 24 |
| 10 | Tottenham HotspurSpurs | 16 | 7 | 2 | 7 | 36 | 19 | 17 | 23 |
| 11 | Brentford | 16 | 7 | 2 | 7 | 32 | 30 | 2 | 23 |
| 12 | Newcastle UnitedNewcastle | 16 | 6 | 5 | 5 | 23 | 21 | 2 | 23 |
| 13 | Manchester UnitedMan Utd | 16 | 6 | 4 | 6 | 21 | 19 | 2 | 22 |
| 14 | West Ham UnitedWest Ham | 16 | 5 | 4 | 7 | 21 | 29 | -8 | 19 |
| 15 | Crystal Palace | 16 | 3 | 7 | 6 | 17 | 21 | -4 | 16 |
| 16 | Everton | 15 | 3 | 6 | 6 | 14 | 21 | -7 | 15 |
| 17 | Leicester CityLeicester | 16 | 3 | 5 | 8 | 21 | 34 | -13 | 14 |
| 18 | Ipswich TownIpswich | 16 | 2 | 6 | 8 | 16 | 28 | -12 | 12 |
| 19 | Wolverhampton WanderersWolves | 16 | 2 | 3 | 11 | 24 | 40 | -16 | 9 |
| 20 | Southampton | 16 | 1 | 2 | 13 | 11 | 36 | -25 | 5 |
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