The Welsh international, 26, has one year remaining on his current deal at the Liberty Stadium.
Taylor, who joined the club in 2010, has made 34 appearances in all competitions this season.
Swans boss Garry Monk is now eager to extend the full-back's stay at the club, according to Sky Sports News.
The Premier League side continue their campaign tonight when they face Arsenal at the Emirates Stadium.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | West Bromwich AlbionWest Brom | 7 | 5 | 1 | 1 | 12 | 5 | 7 | 16 |
| 2 | Sunderland | 7 | 5 | 0 | 2 | 14 | 6 | 8 | 15 |
| 3 | Blackburn RoversBlackburn | 7 | 4 | 3 | 0 | 14 | 6 | 8 | 15 |
| 4 | Burnley | 7 | 4 | 2 | 1 | 13 | 4 | 9 | 14 |
| 5 | Leeds UnitedLeeds | 7 | 4 | 2 | 1 | 12 | 4 | 8 | 14 |
| 6 | Sheffield UnitedSheff Utd | 7 | 4 | 3 | 0 | 9 | 3 | 6 | 13 |
| 7 | Watford | 7 | 4 | 1 | 2 | 12 | 10 | 2 | 13 |
| 8 | Middlesbrough | 7 | 3 | 2 | 2 | 8 | 5 | 3 | 11 |
| 9 | Swansea CitySwansea | 7 | 3 | 2 | 2 | 8 | 5 | 3 | 11 |
| 10 | Norwich CityNorwich | 7 | 3 | 2 | 2 | 11 | 9 | 2 | 11 |
| 11 | Oxford UnitedOxford Utd | 7 | 3 | 1 | 3 | 10 | 8 | 2 | 10 |
| 12 | Hull City | 7 | 2 | 3 | 2 | 9 | 8 | 1 | 9 |
| 13 | Derby CountyDerby | 7 | 3 | 0 | 4 | 10 | 10 | 0 | 9 |
| 14 | Bristol City | 7 | 2 | 3 | 2 | 9 | 13 | -4 | 9 |
| 15 | Millwall | 7 | 2 | 2 | 3 | 12 | 10 | 2 | 8 |
| 16 | Plymouth ArgylePlymouth | 7 | 2 | 2 | 3 | 8 | 11 | -3 | 8 |
| 17 | Queens Park RangersQPR | 7 | 1 | 4 | 2 | 8 | 11 | -3 | 7 |
| 18 | Sheffield WednesdaySheff Weds | 7 | 2 | 1 | 4 | 9 | 14 | -5 | 7 |
| 19 | Luton TownLuton | 7 | 2 | 1 | 4 | 6 | 11 | -5 | 7 |
| 20 | Stoke CityStoke | 7 | 2 | 0 | 5 | 4 | 11 | -7 | 6 |
| 21 | Coventry CityCoventry | 7 | 1 | 2 | 4 | 6 | 11 | -5 | 5 |
| 22 | Preston North EndPreston | 7 | 1 | 2 | 4 | 4 | 12 | -8 | 5 |
| 23 | Portsmouth | 7 | 0 | 4 | 3 | 7 | 13 | -6 | 4 |
| 24 | Cardiff CityCardiff | 7 | 0 | 1 | 6 | 2 | 17 | -15 | 1 |
| > Championship Full Table | |||||||||
