According to BBC Coventry and Warwickshire, Shaw is joined on the list by Oxford boss Chris Wilder, while former Hull City boss Phil Brown is also in the running.
Coventry have picked up just three points from their first five matches in League One.
They face Tranmere Rovers in the league on Saturday.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Sunderland | 13 | 9 | 2 | 2 | 23 | 9 | 14 | 29 |
| 2 | Sheffield UnitedSheff Utd | 14 | 9 | 3 | 2 | 18 | 7 | 11 | 28 |
| 3 | Leeds UnitedLeeds | 13 | 7 | 5 | 1 | 22 | 8 | 14 | 26 |
| 4 | Burnley | 13 | 6 | 5 | 2 | 17 | 6 | 11 | 23 |
| 5 | Watford | 14 | 7 | 1 | 6 | 22 | 22 | 0 | 22 |
| 6 | West Bromwich AlbionWest Brom | 13 | 5 | 6 | 2 | 14 | 8 | 6 | 21 |
| 7 | Middlesbrough | 14 | 6 | 3 | 5 | 18 | 16 | 2 | 21 |
| 8 | Millwall | 13 | 5 | 4 | 4 | 16 | 12 | 4 | 19 |
| 9 | Blackburn RoversBlackburn | 13 | 5 | 4 | 4 | 16 | 14 | 2 | 19 |
| 10 | Swansea CitySwansea | 14 | 5 | 4 | 5 | 11 | 9 | 2 | 19 |
| 11 | Bristol City | 14 | 4 | 7 | 3 | 18 | 19 | -1 | 19 |
| 12 | Norwich CityNorwich | 14 | 4 | 6 | 4 | 23 | 20 | 3 | 18 |
| 13 | Sheffield WednesdaySheff Weds | 14 | 5 | 3 | 6 | 17 | 24 | -7 | 18 |
| 14 | Oxford UnitedOxford Utd | 14 | 4 | 5 | 5 | 17 | 17 | 0 | 17 |
| 15 | Coventry CityCoventry | 13 | 4 | 3 | 6 | 17 | 17 | 0 | 15 |
| 16 | Derby CountyDerby | 13 | 4 | 3 | 6 | 16 | 17 | -1 | 15 |
| 17 | Stoke CityStoke | 13 | 4 | 3 | 6 | 15 | 18 | -3 | 15 |
| 18 | Hull City | 14 | 3 | 6 | 5 | 15 | 18 | -3 | 15 |
| 19 | Cardiff CityCardiff | 13 | 4 | 3 | 6 | 13 | 19 | -6 | 15 |
| 20 | Plymouth ArgylePlymouth | 14 | 4 | 3 | 7 | 14 | 25 | -11 | 15 |
| 21 | Preston North EndPreston | 13 | 3 | 5 | 5 | 14 | 20 | -6 | 14 |
| 22 | Luton TownLuton | 13 | 3 | 3 | 7 | 15 | 21 | -6 | 12 |
| 23 | Queens Park RangersQPR | 14 | 1 | 7 | 6 | 12 | 23 | -11 | 10 |
| 24 | Portsmouth | 14 | 1 | 6 | 7 | 13 | 27 | -14 | 9 |
| > Championship Full Table | |||||||||
