The 29-year-old has scored 30 goals in all competitions for the Championship club this season.
The Cottagers could lodge a bid for the former Brighton & Hove Albion attacker at the end of the campaign, according to The Mirror.
Aston Villa and Norwich City are also thought to be monitoring Murray's situation at Selhurst Park.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Liverpool | 21 | 15 | 5 | 1 | 50 | 20 | 30 | 50 |
| 2 | Arsenal | 22 | 12 | 8 | 2 | 43 | 21 | 22 | 44 |
| 3 | Nottingham ForestNott'm Forest | 22 | 13 | 5 | 4 | 33 | 22 | 11 | 44 |
| 4 | Chelsea | 22 | 11 | 7 | 4 | 44 | 27 | 17 | 40 |
| 5 | Manchester CityMan City | 22 | 11 | 5 | 6 | 44 | 29 | 15 | 38 |
| 6 | Newcastle UnitedNewcastle | 22 | 11 | 5 | 6 | 38 | 26 | 12 | 38 |
| 7 | Bournemouth | 22 | 10 | 7 | 5 | 36 | 26 | 10 | 37 |
| 8 | Aston Villa | 22 | 10 | 6 | 6 | 33 | 34 | -1 | 36 |
| 9 | Brighton & Hove AlbionBrighton | 22 | 8 | 10 | 4 | 35 | 30 | 5 | 34 |
| 10 | Fulham | 22 | 8 | 9 | 5 | 34 | 30 | 4 | 33 |
| 11 | Brentford | 22 | 8 | 4 | 10 | 40 | 39 | 1 | 28 |
| 12 | Crystal Palace | 22 | 6 | 9 | 7 | 25 | 28 | -3 | 27 |
| 13 | Manchester UnitedMan Utd | 22 | 7 | 5 | 10 | 27 | 32 | -5 | 26 |
| 14 | West Ham UnitedWest Ham | 22 | 7 | 5 | 10 | 27 | 43 | -16 | 26 |
| 15 | Tottenham HotspurSpurs | 22 | 7 | 3 | 12 | 45 | 35 | 10 | 24 |
| 16 | Everton | 21 | 4 | 8 | 9 | 18 | 28 | -10 | 20 |
| 17 | Wolverhampton WanderersWolves | 22 | 4 | 4 | 14 | 32 | 51 | -19 | 16 |
| 18 | Ipswich TownIpswich | 22 | 3 | 7 | 12 | 20 | 43 | -23 | 16 |
| 19 | Leicester CityLeicester | 22 | 3 | 5 | 14 | 23 | 48 | -25 | 14 |
| 20 | Southampton | 22 | 1 | 3 | 18 | 15 | 50 | -35 | 6 |
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