Wednesday night's Champions League defeat to Bayer Levekusen was the Blues' fifth defeat in six games in all competitions.
The 34-year-old will now try to split up supposed factions within the dressing room, according to The Mirror.
Assistant coach Roberto Di Matteo is also thought to be unsure about his position at the club and could vacate the role before Christmas.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Liverpool | 7 | 6 | 0 | 1 | 13 | 2 | 11 | 18 |
| 2 | Manchester CityMan City | 7 | 5 | 2 | 0 | 17 | 8 | 9 | 17 |
| 3 | Arsenal | 7 | 5 | 2 | 0 | 15 | 6 | 9 | 17 |
| 4 | Chelsea | 6 | 4 | 1 | 1 | 15 | 7 | 8 | 13 |
| 5 | Aston Villa | 6 | 4 | 1 | 1 | 12 | 9 | 3 | 13 |
| 6 | Newcastle UnitedNewcastle | 7 | 3 | 3 | 1 | 8 | 7 | 1 | 12 |
| 7 | Fulham | 7 | 3 | 2 | 2 | 10 | 8 | 2 | 11 |
| 8 | Tottenham HotspurSpurs | 6 | 3 | 1 | 2 | 12 | 5 | 7 | 10 |
| 9 | Brentford | 7 | 3 | 1 | 3 | 13 | 13 | 0 | 10 |
| 10 | Brighton & Hove AlbionBrighton | 6 | 2 | 3 | 1 | 10 | 8 | 2 | 9 |
| 11 | Nottingham ForestNott'm Forest | 6 | 2 | 3 | 1 | 6 | 5 | 1 | 9 |
| 12 | West Ham UnitedWest Ham | 7 | 2 | 2 | 3 | 10 | 11 | -1 | 8 |
| 13 | Bournemouth | 7 | 2 | 2 | 3 | 8 | 10 | -2 | 8 |
| 14 | Manchester UnitedMan Utd | 6 | 2 | 1 | 3 | 5 | 8 | -3 | 7 |
| 15 | Leicester CityLeicester | 7 | 1 | 3 | 3 | 9 | 12 | -3 | 6 |
| 16 | Everton | 7 | 1 | 2 | 4 | 7 | 15 | -8 | 5 |
| 17 | Ipswich TownIpswich | 7 | 0 | 4 | 3 | 6 | 14 | -8 | 4 |
| 18 | Crystal Palace | 7 | 0 | 3 | 4 | 5 | 10 | -5 | 3 |
| 19 | Southampton | 7 | 0 | 1 | 6 | 4 | 15 | -11 | 1 |
| 20 | Wolverhampton WanderersWolves | 7 | 0 | 1 | 6 | 9 | 21 | -12 | 1 |
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