The 32-year-old is a free agent after leaving the Camp Nou at the end of last season.
According to the Daily Star, Reds manager Brendan Rodgers is interested in signing the veteran keeper to provide competition for current first-choice stopper Simon Mignolet.
Valdes, a mainstay at the Blaugrana between 2002 and 2014, is currently sidelined with a knee injury.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Arsenal | 35 | 25 | 5 | 5 | 85 | 28 | 57 | 80 |
| 2 | Manchester CityMan City | 34 | 24 | 7 | 3 | 82 | 32 | 50 | 79 |
| 3 | Liverpool | 35 | 22 | 9 | 4 | 77 | 36 | 41 | 75 |
| 4 | Aston Villa | 35 | 20 | 7 | 8 | 73 | 52 | 21 | 67 |
| 5 | Tottenham HotspurSpurs | 33 | 18 | 6 | 9 | 67 | 52 | 15 | 60 |
| 6 | Manchester UnitedMan Utd | 34 | 16 | 6 | 12 | 52 | 51 | 1 | 54 |
| 7 | Newcastle UnitedNewcastle | 34 | 16 | 5 | 13 | 74 | 55 | 19 | 53 |
| 8 | West Ham UnitedWest Ham | 35 | 13 | 10 | 12 | 56 | 65 | -9 | 49 |
| 9 | Chelsea | 33 | 13 | 9 | 11 | 63 | 59 | 4 | 48 |
| 10 | Bournemouth | 35 | 13 | 9 | 13 | 52 | 60 | -8 | 48 |
| 11 | Wolverhampton WanderersWolves | 35 | 13 | 7 | 15 | 48 | 55 | -7 | 46 |
| 12 | Brighton & Hove AlbionBrighton | 34 | 11 | 11 | 12 | 52 | 57 | -5 | 44 |
| 13 | Fulham | 35 | 12 | 7 | 16 | 51 | 55 | -4 | 43 |
| 14 | Crystal Palace | 35 | 10 | 10 | 15 | 45 | 57 | -12 | 40 |
| 15 | Everton | 35 | 12 | 8 | 15 | 37 | 48 | -11 | 36 |
| 16 | Brentford | 35 | 9 | 8 | 18 | 52 | 60 | -8 | 35 |
| 17 | Nottingham ForestNott'm Forest | 35 | 7 | 9 | 19 | 42 | 62 | -20 | 26 |
| 18 | Luton TownLuton | 35 | 6 | 7 | 22 | 48 | 77 | -29 | 25 |
| 19 | Burnley | 35 | 5 | 9 | 21 | 38 | 70 | -32 | 24 |
| R | Sheffield UnitedSheff Utd | 35 | 3 | 7 | 25 | 34 | 97 | -63 | 16 |
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