The 30-year-old is due to become a free agent in the summer when his contract at Parkhead expires.
He recently revealed that talks over fresh terms were underway, but no agreement has been reached.
According to the Scottish Sun, that has alerted English Championship outfit Derby.
Mulgrew rejoined the Bhoys in 2010 following a spell with Aberdeen.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Leeds UnitedLeeds | 16 | 9 | 5 | 2 | 28 | 12 | 16 | 32 |
| 2 | Sunderland | 16 | 9 | 5 | 2 | 26 | 12 | 14 | 32 |
| 3 | Sheffield UnitedSheff Utd | 16 | 10 | 4 | 2 | 21 | 9 | 12 | 32 |
| 4 | Burnley | 16 | 8 | 6 | 2 | 19 | 6 | 13 | 30 |
| 5 | Middlesbrough | 16 | 8 | 3 | 5 | 29 | 19 | 10 | 27 |
| 6 | West Bromwich AlbionWest Brom | 16 | 6 | 8 | 2 | 18 | 11 | 7 | 26 |
| 7 | Watford | 16 | 8 | 2 | 6 | 25 | 24 | 1 | 26 |
| 8 | Millwall | 16 | 6 | 6 | 4 | 19 | 14 | 5 | 24 |
| 9 | Blackburn RoversBlackburn | 15 | 6 | 4 | 5 | 19 | 17 | 2 | 22 |
| 10 | Bristol City | 16 | 5 | 7 | 4 | 20 | 20 | 0 | 22 |
| 11 | Derby CountyDerby | 16 | 5 | 5 | 6 | 20 | 20 | 0 | 20 |
| 12 | Stoke CityStoke | 16 | 5 | 5 | 6 | 19 | 20 | -1 | 20 |
| 13 | Norwich CityNorwich | 16 | 4 | 7 | 5 | 25 | 24 | 1 | 19 |
| 14 | Swansea CitySwansea | 16 | 5 | 4 | 7 | 14 | 14 | 0 | 19 |
| 15 | Sheffield WednesdaySheff Weds | 16 | 5 | 4 | 7 | 18 | 26 | -8 | 19 |
| 16 | Luton TownLuton | 16 | 5 | 3 | 8 | 18 | 26 | -8 | 18 |
| 17 | Coventry CityCoventry | 16 | 4 | 5 | 7 | 22 | 23 | -1 | 17 |
| 18 | Oxford UnitedOxford Utd | 16 | 4 | 5 | 7 | 19 | 24 | -5 | 17 |
| 19 | Plymouth ArgylePlymouth | 16 | 4 | 5 | 7 | 17 | 28 | -11 | 17 |
| 20 | Preston North EndPreston | 16 | 3 | 7 | 6 | 16 | 24 | -8 | 16 |
| 21 | Cardiff CityCardiff | 16 | 4 | 4 | 8 | 15 | 24 | -9 | 16 |
| 22 | Hull City | 16 | 3 | 6 | 7 | 16 | 21 | -5 | 15 |
| 23 | Portsmouth | 15 | 2 | 6 | 7 | 16 | 28 | -12 | 12 |
| 24 | Queens Park RangersQPR | 16 | 1 | 8 | 7 | 13 | 26 | -13 | 11 |
| > Championship Full Table | |||||||||
