The Telegraph states that the 71-year-old could announce plans to step down by the end of the week.
The club is yet to comment on the speculation, which emerged during a players versus coaches golf day at Dunham Massey this afternoon.
The Scot recently guided United to their 20th league title and the 13th during his reign at Old Trafford.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Liverpool | 22 | 16 | 5 | 1 | 54 | 21 | 33 | 53 |
| 2 | Arsenal | 23 | 13 | 8 | 2 | 44 | 21 | 23 | 47 |
| 3 | Nottingham ForestNott'm Forest | 23 | 13 | 5 | 5 | 33 | 27 | 6 | 44 |
| 4 | Manchester CityMan City | 23 | 12 | 5 | 6 | 47 | 30 | 17 | 41 |
| 5 | Newcastle UnitedNewcastle | 23 | 12 | 5 | 6 | 41 | 27 | 14 | 41 |
| 6 | Chelsea | 23 | 11 | 7 | 5 | 45 | 30 | 15 | 40 |
| 7 | Bournemouth | 23 | 11 | 7 | 5 | 41 | 26 | 15 | 40 |
| 8 | Aston Villa | 23 | 10 | 7 | 6 | 34 | 35 | -1 | 37 |
| 9 | Brighton & Hove AlbionBrighton | 23 | 8 | 10 | 5 | 35 | 31 | 4 | 34 |
| 10 | Fulham | 23 | 8 | 9 | 6 | 34 | 31 | 3 | 33 |
| 11 | Brentford | 23 | 9 | 4 | 10 | 42 | 40 | 2 | 31 |
| 12 | Manchester UnitedMan Utd | 23 | 8 | 5 | 10 | 28 | 32 | -4 | 29 |
| 13 | Crystal Palace | 23 | 6 | 9 | 8 | 26 | 30 | -4 | 27 |
| 14 | West Ham UnitedWest Ham | 23 | 7 | 6 | 10 | 28 | 44 | -16 | 27 |
| 15 | Tottenham HotspurSpurs | 23 | 7 | 3 | 13 | 46 | 37 | 9 | 24 |
| 16 | Everton | 22 | 5 | 8 | 9 | 19 | 28 | -9 | 23 |
| 17 | Leicester CityLeicester | 23 | 4 | 5 | 14 | 25 | 49 | -24 | 17 |
| 18 | Wolverhampton WanderersWolves | 23 | 4 | 4 | 15 | 32 | 52 | -20 | 16 |
| 19 | Ipswich TownIpswich | 23 | 3 | 7 | 13 | 21 | 47 | -26 | 16 |
| 20 | Southampton | 23 | 1 | 3 | 19 | 16 | 53 | -37 | 6 |
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