The 25-year-old is currently a free agent, having refused to transfer his Rangers contract to Charles Green's newco.
Stoke City, West Ham United and Blackburn Rovers are also said to be interested in Naismith's signature.
However, the player has made it clear that Goodison Park is his preferred destination, according to The Sun.
Naismith made 98 SPL appearances during five years at the Ibrox club, scoring 28 goals.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Liverpool | 7 | 6 | 0 | 1 | 13 | 2 | 11 | 18 |
| 2 | Manchester CityMan City | 7 | 5 | 2 | 0 | 17 | 8 | 9 | 17 |
| 3 | Arsenal | 7 | 5 | 2 | 0 | 15 | 6 | 9 | 17 |
| 4 | Chelsea | 6 | 4 | 1 | 1 | 15 | 7 | 8 | 13 |
| 5 | Aston Villa | 6 | 4 | 1 | 1 | 12 | 9 | 3 | 13 |
| 6 | Newcastle UnitedNewcastle | 7 | 3 | 3 | 1 | 8 | 7 | 1 | 12 |
| 7 | Fulham | 7 | 3 | 2 | 2 | 10 | 8 | 2 | 11 |
| 8 | Tottenham HotspurSpurs | 6 | 3 | 1 | 2 | 12 | 5 | 7 | 10 |
| 9 | Brentford | 7 | 3 | 1 | 3 | 13 | 13 | 0 | 10 |
| 10 | Brighton & Hove AlbionBrighton | 6 | 2 | 3 | 1 | 10 | 8 | 2 | 9 |
| 11 | Nottingham ForestNott'm Forest | 6 | 2 | 3 | 1 | 6 | 5 | 1 | 9 |
| 12 | West Ham UnitedWest Ham | 7 | 2 | 2 | 3 | 10 | 11 | -1 | 8 |
| 13 | Bournemouth | 7 | 2 | 2 | 3 | 8 | 10 | -2 | 8 |
| 14 | Manchester UnitedMan Utd | 6 | 2 | 1 | 3 | 5 | 8 | -3 | 7 |
| 15 | Leicester CityLeicester | 7 | 1 | 3 | 3 | 9 | 12 | -3 | 6 |
| 16 | Everton | 7 | 1 | 2 | 4 | 7 | 15 | -8 | 5 |
| 17 | Ipswich TownIpswich | 7 | 0 | 4 | 3 | 6 | 14 | -8 | 4 |
| 18 | Crystal Palace | 7 | 0 | 3 | 4 | 5 | 10 | -5 | 3 |
| 19 | Southampton | 7 | 0 | 1 | 6 | 4 | 15 | -11 | 1 |
| 20 | Wolverhampton WanderersWolves | 7 | 0 | 1 | 6 | 9 | 21 | -12 | 1 |
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