The Australian, who has played 10 times for the Reds this season in place of the injured Pepe Reina, will be a free agent in the summer.
Manager Brendan Rodgers now wants to extend the 30-year-old's stay at Anfield, according to The Mirror.
Jones joined the Merseysiders from Middlesbrough in 2010 for £2.3m.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Liverpool | 20 | 14 | 5 | 1 | 48 | 20 | 28 | 47 |
| 2 | Arsenal | 21 | 12 | 7 | 2 | 41 | 19 | 22 | 43 |
| 3 | Nottingham ForestNott'm Forest | 21 | 12 | 5 | 4 | 30 | 20 | 10 | 41 |
| 4 | Newcastle UnitedNewcastle | 21 | 11 | 5 | 5 | 37 | 22 | 15 | 38 |
| 5 | Chelsea | 21 | 10 | 7 | 4 | 41 | 26 | 15 | 37 |
| 6 | Manchester CityMan City | 21 | 10 | 5 | 6 | 38 | 29 | 9 | 35 |
| 7 | Aston Villa | 21 | 10 | 5 | 6 | 31 | 32 | -1 | 35 |
| 8 | Bournemouth | 21 | 9 | 7 | 5 | 32 | 25 | 7 | 34 |
| 9 | Fulham | 21 | 7 | 9 | 5 | 32 | 30 | 2 | 30 |
| 10 | Brentford | 21 | 8 | 4 | 9 | 40 | 37 | 3 | 28 |
| 11 | Brighton & Hove AlbionBrighton | 20 | 6 | 10 | 4 | 30 | 29 | 1 | 28 |
| 12 | West Ham UnitedWest Ham | 21 | 7 | 5 | 9 | 27 | 41 | -14 | 26 |
| 13 | Tottenham HotspurSpurs | 21 | 7 | 3 | 11 | 43 | 32 | 11 | 24 |
| 14 | Crystal Palace | 21 | 5 | 9 | 7 | 23 | 28 | -5 | 24 |
| 15 | Manchester UnitedMan Utd | 20 | 6 | 5 | 9 | 23 | 28 | -5 | 23 |
| 16 | Everton | 20 | 3 | 8 | 9 | 15 | 26 | -11 | 17 |
| 17 | Ipswich TownIpswich | 20 | 3 | 7 | 10 | 20 | 35 | -15 | 16 |
| 18 | Wolverhampton WanderersWolves | 21 | 4 | 4 | 13 | 31 | 48 | -17 | 16 |
| 19 | Leicester CityLeicester | 21 | 3 | 5 | 13 | 23 | 46 | -23 | 14 |
| 20 | Southampton | 20 | 1 | 3 | 16 | 12 | 44 | -32 | 6 |
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