The striker, who is the son of former England international Nick Barmby, was United's leading scorer for the Under-18 side during the 2012-13 campaign.
The 19-year-old recently had a loan spell at Hartlepool United in League Two, scoring five goals in 17 appearances.
Barmby will be added to the Foxes' development squad.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Manchester CityMan City | 32 | 22 | 7 | 3 | 76 | 32 | 44 | 73 |
| 2 | Arsenal | 32 | 22 | 5 | 5 | 75 | 26 | 49 | 71 |
| 3 | Liverpool | 32 | 21 | 8 | 3 | 72 | 31 | 41 | 71 |
| 4 | Aston Villa | 33 | 19 | 6 | 8 | 68 | 49 | 19 | 63 |
| 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 | 33 | 13 | 9 | 11 | 52 | 58 | -6 | 48 |
| 9 | Chelsea | 31 | 13 | 8 | 10 | 61 | 52 | 9 | 47 |
| 10 | Brighton & Hove AlbionBrighton | 32 | 11 | 11 | 10 | 52 | 50 | 2 | 44 |
| 11 | Wolverhampton WanderersWolves | 32 | 12 | 7 | 13 | 46 | 51 | -5 | 43 |
| 12 | Fulham | 33 | 12 | 6 | 15 | 49 | 51 | -2 | 42 |
| 13 | Bournemouth | 32 | 11 | 9 | 12 | 47 | 57 | -10 | 42 |
| 14 | Crystal Palace | 32 | 8 | 9 | 15 | 37 | 54 | -17 | 33 |
| 15 | Brentford | 33 | 8 | 8 | 17 | 47 | 58 | -11 | 32 |
| 16 | Everton | 32 | 9 | 8 | 15 | 32 | 48 | -16 | 27 |
| 17 | Nottingham ForestNott'm Forest | 33 | 7 | 9 | 17 | 42 | 58 | -16 | 26 |
| 18 | Luton TownLuton | 33 | 6 | 7 | 20 | 46 | 70 | -24 | 25 |
| 19 | Burnley | 33 | 4 | 8 | 21 | 33 | 68 | -35 | 20 |
| 20 | Sheffield UnitedSheff Utd | 32 | 3 | 7 | 22 | 30 | 84 | -54 | 16 |
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