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 | 6 | 5 | 0 | 1 | 12 | 2 | 10 | 15 |
| 2 | Manchester CityMan City | 6 | 4 | 2 | 0 | 14 | 6 | 8 | 14 |
| 3 | Arsenal | 6 | 4 | 2 | 0 | 12 | 5 | 7 | 14 |
| 4 | Chelsea | 6 | 4 | 1 | 1 | 15 | 7 | 8 | 13 |
| 5 | Aston Villa | 6 | 4 | 1 | 1 | 12 | 9 | 3 | 13 |
| 6 | Fulham | 6 | 3 | 2 | 1 | 8 | 5 | 3 | 11 |
| 7 | Newcastle UnitedNewcastle | 6 | 3 | 2 | 1 | 8 | 7 | 1 | 11 |
| 8 | Tottenham HotspurSpurs | 6 | 3 | 1 | 2 | 12 | 5 | 7 | 10 |
| 9 | Brighton & Hove AlbionBrighton | 6 | 2 | 3 | 1 | 10 | 8 | 2 | 9 |
| 10 | Nottingham ForestNott'm Forest | 6 | 2 | 3 | 1 | 6 | 5 | 1 | 9 |
| 11 | Bournemouth | 6 | 2 | 2 | 2 | 8 | 9 | -1 | 8 |
| 12 | Brentford | 6 | 2 | 1 | 3 | 8 | 10 | -2 | 7 |
| 13 | Manchester UnitedMan Utd | 6 | 2 | 1 | 3 | 5 | 8 | -3 | 7 |
| 14 | West Ham UnitedWest Ham | 6 | 1 | 2 | 3 | 6 | 10 | -4 | 5 |
| 15 | Ipswich TownIpswich | 6 | 0 | 4 | 2 | 5 | 10 | -5 | 4 |
| 16 | Everton | 6 | 1 | 1 | 4 | 7 | 15 | -8 | 4 |
| 17 | Leicester CityLeicester | 6 | 0 | 3 | 3 | 8 | 12 | -4 | 3 |
| 18 | Crystal Palace | 6 | 0 | 3 | 3 | 5 | 9 | -4 | 3 |
| 19 | Southampton | 6 | 0 | 1 | 5 | 3 | 12 | -9 | 1 |
| 20 | Wolverhampton WanderersWolves | 6 | 0 | 1 | 5 | 6 | 16 | -10 | 1 |
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