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 | 16 | 12 | 3 | 1 | 37 | 16 | 21 | 39 |
| 2 | Chelsea | 17 | 10 | 5 | 2 | 37 | 19 | 18 | 35 |
| 3 | Arsenal | 17 | 9 | 6 | 2 | 34 | 16 | 18 | 33 |
| 4 | Nottingham ForestNott'm Forest | 17 | 9 | 4 | 4 | 23 | 19 | 4 | 31 |
| 5 | Bournemouth | 17 | 8 | 4 | 5 | 27 | 21 | 6 | 28 |
| 6 | Aston Villa | 17 | 8 | 4 | 5 | 26 | 26 | 0 | 28 |
| 7 | Manchester CityMan City | 17 | 8 | 3 | 6 | 29 | 25 | 4 | 27 |
| 8 | Newcastle UnitedNewcastle | 17 | 7 | 5 | 5 | 27 | 21 | 6 | 26 |
| 9 | Fulham | 17 | 6 | 7 | 4 | 24 | 22 | 2 | 25 |
| 10 | Brighton & Hove AlbionBrighton | 17 | 6 | 7 | 4 | 27 | 26 | 1 | 25 |
| 11 | Tottenham HotspurSpurs | 17 | 7 | 2 | 8 | 39 | 25 | 14 | 23 |
| 12 | Brentford | 17 | 7 | 2 | 8 | 32 | 32 | 0 | 23 |
| 13 | Manchester UnitedMan Utd | 17 | 6 | 4 | 7 | 21 | 22 | -1 | 22 |
| 14 | West Ham UnitedWest Ham | 17 | 5 | 5 | 7 | 22 | 30 | -8 | 20 |
| 15 | Everton | 16 | 3 | 7 | 6 | 14 | 21 | -7 | 16 |
| 16 | Crystal Palace | 17 | 3 | 7 | 7 | 18 | 26 | -8 | 16 |
| 17 | Leicester CityLeicester | 17 | 3 | 5 | 9 | 21 | 37 | -16 | 14 |
| 18 | Wolverhampton WanderersWolves | 17 | 3 | 3 | 11 | 27 | 40 | -13 | 12 |
| 19 | Ipswich TownIpswich | 17 | 2 | 6 | 9 | 16 | 32 | -16 | 12 |
| 20 | Southampton | 17 | 1 | 3 | 13 | 11 | 36 | -25 | 6 |
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