The Reds boss is targeting the Newcastle midfielder in a £5 million deal, according to the Daily Mail.
The newspaper says that Dalglish "recognises the move would be controversial" but believes Barton could "add an edge to his side" and work well with Andy Carroll.
Barton was red carded at Anfield in 2009 after a fierce tackle on Xabi Alonso.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Liverpool | 14 | 11 | 2 | 1 | 29 | 11 | 18 | 35 |
| 2 | Chelsea | 15 | 9 | 4 | 2 | 35 | 18 | 17 | 31 |
| 3 | Arsenal | 15 | 8 | 5 | 2 | 29 | 15 | 14 | 29 |
| 4 | Manchester CityMan City | 15 | 8 | 3 | 4 | 27 | 21 | 6 | 27 |
| 5 | Nottingham ForestNott'm Forest | 15 | 7 | 4 | 4 | 19 | 18 | 1 | 25 |
| 6 | Aston Villa | 15 | 7 | 4 | 4 | 23 | 23 | 0 | 25 |
| 7 | Brighton & Hove AlbionBrighton | 15 | 6 | 6 | 3 | 25 | 22 | 3 | 24 |
| 8 | Bournemouth | 15 | 7 | 3 | 5 | 23 | 20 | 3 | 24 |
| 9 | Brentford | 15 | 7 | 2 | 6 | 31 | 28 | 3 | 23 |
| 10 | Fulham | 15 | 6 | 5 | 4 | 22 | 20 | 2 | 23 |
| 11 | Tottenham HotspurSpurs | 15 | 6 | 2 | 7 | 31 | 19 | 12 | 20 |
| 12 | Newcastle UnitedNewcastle | 15 | 5 | 5 | 5 | 19 | 21 | -2 | 20 |
| 13 | Manchester UnitedMan Utd | 15 | 5 | 4 | 6 | 19 | 18 | 1 | 19 |
| 14 | West Ham UnitedWest Ham | 15 | 5 | 3 | 7 | 20 | 28 | -8 | 18 |
| 15 | Everton | 14 | 3 | 5 | 6 | 14 | 21 | -7 | 14 |
| 16 | Leicester CityLeicester | 15 | 3 | 5 | 7 | 21 | 30 | -9 | 14 |
| 17 | Crystal Palace | 15 | 2 | 7 | 6 | 14 | 20 | -6 | 13 |
| 18 | Ipswich TownIpswich | 15 | 1 | 6 | 8 | 14 | 27 | -13 | 9 |
| 19 | Wolverhampton WanderersWolves | 15 | 2 | 3 | 10 | 23 | 38 | -15 | 9 |
| 20 | Southampton | 15 | 1 | 2 | 12 | 11 | 31 | -20 | 5 |
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