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 | Arsenal | 36 | 26 | 5 | 5 | 88 | 28 | 60 | 83 |
| 2 | Manchester CityMan City | 35 | 25 | 7 | 3 | 87 | 33 | 54 | 82 |
| 3 | Liverpool | 36 | 23 | 9 | 4 | 81 | 38 | 43 | 78 |
| 4 | Aston Villa | 36 | 20 | 7 | 9 | 73 | 53 | 20 | 67 |
| 5 | Tottenham HotspurSpurs | 35 | 18 | 6 | 11 | 69 | 58 | 11 | 60 |
| 6 | Newcastle UnitedNewcastle | 35 | 17 | 5 | 13 | 78 | 56 | 22 | 56 |
| 7 | Chelsea | 35 | 15 | 9 | 11 | 70 | 59 | 11 | 54 |
| 8 | Manchester UnitedMan Utd | 35 | 16 | 6 | 13 | 52 | 55 | -3 | 54 |
| 9 | West Ham UnitedWest Ham | 36 | 13 | 10 | 13 | 56 | 70 | -14 | 49 |
| 10 | Bournemouth | 36 | 13 | 9 | 14 | 52 | 63 | -11 | 48 |
| 11 | Brighton & Hove AlbionBrighton | 35 | 12 | 11 | 12 | 53 | 57 | -4 | 47 |
| 12 | Wolverhampton WanderersWolves | 36 | 13 | 7 | 16 | 49 | 60 | -11 | 46 |
| 13 | Fulham | 36 | 12 | 8 | 16 | 51 | 55 | -4 | 44 |
| 14 | Crystal Palace | 36 | 11 | 10 | 15 | 49 | 57 | -8 | 43 |
| 15 | Everton | 36 | 12 | 9 | 15 | 38 | 49 | -11 | 37 |
| 16 | Brentford | 36 | 9 | 9 | 18 | 52 | 60 | -8 | 36 |
| 17 | Nottingham ForestNott'm Forest | 36 | 8 | 9 | 19 | 45 | 63 | -18 | 29 |
| 18 | Luton TownLuton | 36 | 6 | 8 | 22 | 49 | 78 | -29 | 26 |
| 19 | Burnley | 36 | 5 | 9 | 22 | 39 | 74 | -35 | 24 |
| R | Sheffield UnitedSheff Utd | 36 | 3 | 7 | 26 | 35 | 100 | -65 | 16 |
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