Reds boss Brendan Rodgers wants the Bosnian to compete with Simon Mignolet for first-team football next season, according to the Daily Star.
Begovic's future at Stoke has been called into question after he was left out of the Potters' 2-0 defeat to Swansea City last weekend in favour of Jack Butland.
The 27-year-old has 12 months remaining on his contract.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Liverpool | 23 | 17 | 5 | 1 | 56 | 21 | 35 | 56 |
| 2 | Arsenal | 24 | 14 | 8 | 2 | 49 | 22 | 27 | 50 |
| 3 | Nottingham ForestNott'm Forest | 24 | 14 | 5 | 5 | 40 | 27 | 13 | 47 |
| 4 | Chelsea | 24 | 12 | 7 | 5 | 47 | 31 | 16 | 43 |
| 5 | Manchester CityMan City | 24 | 12 | 5 | 7 | 48 | 35 | 13 | 41 |
| 6 | Newcastle UnitedNewcastle | 24 | 12 | 5 | 7 | 42 | 29 | 13 | 41 |
| 7 | Bournemouth | 24 | 11 | 7 | 6 | 41 | 28 | 13 | 40 |
| 8 | Aston Villa | 24 | 10 | 7 | 7 | 34 | 37 | -3 | 37 |
| 9 | Fulham | 24 | 9 | 9 | 6 | 36 | 32 | 4 | 36 |
| 10 | Brighton & Hove AlbionBrighton | 24 | 8 | 10 | 6 | 35 | 38 | -3 | 34 |
| 11 | Brentford | 24 | 9 | 4 | 11 | 42 | 42 | 0 | 31 |
| 12 | Crystal Palace | 24 | 7 | 9 | 8 | 28 | 30 | -2 | 30 |
| 13 | Manchester UnitedMan Utd | 24 | 8 | 5 | 11 | 28 | 34 | -6 | 29 |
| 14 | Tottenham HotspurSpurs | 24 | 8 | 3 | 13 | 48 | 37 | 11 | 27 |
| 15 | West Ham UnitedWest Ham | 24 | 7 | 6 | 11 | 29 | 46 | -17 | 27 |
| 16 | Everton | 23 | 6 | 8 | 9 | 23 | 28 | -5 | 26 |
| 17 | Wolverhampton WanderersWolves | 24 | 5 | 4 | 15 | 34 | 52 | -18 | 19 |
| 18 | Leicester CityLeicester | 24 | 4 | 5 | 15 | 25 | 53 | -28 | 17 |
| 19 | Ipswich TownIpswich | 24 | 3 | 7 | 14 | 22 | 49 | -27 | 16 |
| 20 | Southampton | 24 | 2 | 3 | 19 | 18 | 54 | -36 | 9 |
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