The 18-year-old has made a big impression since breaking into the first team in February, having scored seven goals in 12 appearances.
His current deal is due to expire at the end of next season, which has prompted the Red Devils to begin negotiations, according to TransferMarketWeb.
The report adds that Rashford's new terms are likely to see him pocket around £14,000 a week at Old Trafford.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Arsenal | 34 | 24 | 5 | 5 | 82 | 26 | 56 | 77 |
| 2 | Manchester CityMan City | 33 | 23 | 7 | 3 | 80 | 32 | 48 | 76 |
| 3 | Liverpool | 35 | 22 | 9 | 4 | 77 | 36 | 41 | 75 |
| 4 | Aston Villa | 34 | 20 | 6 | 8 | 71 | 50 | 21 | 66 |
| 5 | Tottenham HotspurSpurs | 32 | 18 | 6 | 8 | 65 | 49 | 16 | 60 |
| 6 | Manchester UnitedMan Utd | 34 | 16 | 6 | 12 | 52 | 51 | 1 | 54 |
| 7 | Newcastle UnitedNewcastle | 34 | 16 | 5 | 13 | 74 | 55 | 19 | 53 |
| 8 | West Ham UnitedWest Ham | 35 | 13 | 10 | 12 | 56 | 65 | -9 | 49 |
| 9 | Chelsea | 32 | 13 | 8 | 11 | 61 | 57 | 4 | 47 |
| 10 | Wolverhampton WanderersWolves | 35 | 13 | 7 | 15 | 48 | 55 | -7 | 46 |
| 11 | Bournemouth | 34 | 12 | 9 | 13 | 49 | 60 | -11 | 45 |
| 12 | Brighton & Hove AlbionBrighton | 33 | 11 | 11 | 11 | 52 | 54 | -2 | 44 |
| 13 | Fulham | 35 | 12 | 7 | 16 | 51 | 55 | -4 | 43 |
| 14 | Crystal Palace | 35 | 10 | 10 | 15 | 45 | 57 | -12 | 40 |
| 15 | Brentford | 34 | 9 | 8 | 17 | 52 | 59 | -7 | 35 |
| 16 | Everton | 34 | 11 | 8 | 15 | 36 | 48 | -12 | 33 |
| 17 | Nottingham ForestNott'm Forest | 34 | 7 | 9 | 18 | 42 | 60 | -18 | 26 |
| 18 | Luton TownLuton | 35 | 6 | 7 | 22 | 48 | 77 | -29 | 25 |
| 19 | Burnley | 35 | 5 | 9 | 21 | 38 | 70 | -32 | 24 |
| 20 | Sheffield UnitedSheff Utd | 35 | 3 | 7 | 25 | 34 | 97 | -63 | 16 |
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