The Merseyside club have had a positive start to the season, recording a 1-0 win over Manchester United and a 3-1 victory over Aston Villa.
"If we can keep everyone fit, we can be challenging for European football," the Daily Star quotes Neville as saying.
Everton travel to West Bromwich Albion on Saturday.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Arsenal | 34 | 24 | 5 | 5 | 82 | 26 | 56 | 77 |
| 2 | Liverpool | 33 | 22 | 8 | 3 | 75 | 32 | 43 | 74 |
| 3 | Manchester CityMan City | 32 | 22 | 7 | 3 | 76 | 32 | 44 | 73 |
| 4 | Aston Villa | 34 | 20 | 6 | 8 | 71 | 50 | 21 | 66 |
| 5 | Tottenham HotspurSpurs | 32 | 18 | 6 | 8 | 65 | 49 | 16 | 60 |
| 6 | Newcastle UnitedNewcastle | 32 | 15 | 5 | 12 | 69 | 52 | 17 | 50 |
| 7 | Manchester UnitedMan Utd | 32 | 15 | 5 | 12 | 47 | 48 | -1 | 50 |
| 8 | West Ham UnitedWest Ham | 34 | 13 | 9 | 12 | 54 | 63 | -9 | 48 |
| 9 | Chelsea | 32 | 13 | 8 | 11 | 61 | 57 | 4 | 47 |
| 10 | Brighton & Hove AlbionBrighton | 32 | 11 | 11 | 10 | 52 | 50 | 2 | 44 |
| 11 | Wolverhampton WanderersWolves | 33 | 12 | 7 | 14 | 46 | 53 | -7 | 43 |
| 12 | Fulham | 34 | 12 | 6 | 16 | 50 | 54 | -4 | 42 |
| 13 | Bournemouth | 33 | 11 | 9 | 13 | 48 | 60 | -12 | 42 |
| 14 | Crystal Palace | 33 | 9 | 9 | 15 | 42 | 56 | -14 | 36 |
| 15 | Brentford | 34 | 9 | 8 | 17 | 52 | 59 | -7 | 35 |
| 16 | Everton | 33 | 10 | 8 | 15 | 34 | 48 | -14 | 30 |
| 17 | Nottingham ForestNott'm Forest | 34 | 7 | 9 | 18 | 42 | 60 | -18 | 26 |
| 18 | Luton TownLuton | 34 | 6 | 7 | 21 | 47 | 75 | -28 | 25 |
| 19 | Burnley | 34 | 5 | 8 | 21 | 37 | 69 | -32 | 23 |
| 20 | Sheffield UnitedSheff Utd | 33 | 3 | 7 | 23 | 31 | 88 | -57 | 16 |
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