Reds manager Kenny Dalglish is thought to be keen on the duo, according to radio station Cadena Ser.
The situation of both players with the Spanish side is unclear due to the recent arrival of manager Diego Simeone.
Godin, 25, has been with Atletico since summer 2010, while 22-year-old Dominguez came up through the club's youth academy.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Liverpool | 11 | 9 | 1 | 1 | 21 | 6 | 15 | 28 |
| 2 | Manchester CityMan City | 11 | 7 | 2 | 2 | 22 | 13 | 9 | 23 |
| 3 | Nottingham ForestNott'm Forest | 10 | 5 | 4 | 1 | 14 | 7 | 7 | 19 |
| 4 | Brighton & Hove AlbionBrighton | 11 | 5 | 4 | 2 | 19 | 15 | 4 | 19 |
| 5 | Chelsea | 10 | 5 | 3 | 2 | 20 | 12 | 8 | 18 |
| 6 | Arsenal | 10 | 5 | 3 | 2 | 17 | 11 | 6 | 18 |
| 7 | Fulham | 11 | 5 | 3 | 3 | 16 | 13 | 3 | 18 |
| 8 | Aston Villa | 11 | 5 | 3 | 3 | 17 | 17 | 0 | 18 |
| 9 | Tottenham HotspurSpurs | 10 | 5 | 1 | 4 | 22 | 11 | 11 | 16 |
| 10 | Brentford | 11 | 5 | 1 | 5 | 22 | 22 | 0 | 16 |
| 11 | Bournemouth | 11 | 4 | 3 | 4 | 15 | 15 | 0 | 15 |
| 12 | Newcastle UnitedNewcastle | 10 | 4 | 3 | 3 | 10 | 10 | 0 | 15 |
| 13 | Manchester UnitedMan Utd | 10 | 3 | 3 | 4 | 9 | 12 | -3 | 12 |
| 14 | West Ham UnitedWest Ham | 11 | 3 | 3 | 5 | 13 | 19 | -6 | 12 |
| 15 | Leicester CityLeicester | 10 | 2 | 4 | 4 | 14 | 18 | -4 | 10 |
| 16 | Everton | 11 | 2 | 4 | 5 | 10 | 17 | -7 | 10 |
| 17 | Crystal Palace | 11 | 1 | 4 | 6 | 8 | 15 | -7 | 7 |
| 18 | Wolverhampton WanderersWolves | 11 | 1 | 3 | 7 | 16 | 27 | -11 | 6 |
| 19 | Ipswich TownIpswich | 10 | 0 | 5 | 5 | 10 | 21 | -11 | 5 |
| 20 | Southampton | 11 | 1 | 1 | 9 | 7 | 21 | -14 | 4 |
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