The 23-year-old has found first-team opportunities limited by the form of Ben Davies since breaking his ankle against Sunderland in September 2012.
Swansea turned down a £1m offer for the full-back from Newcastle in June 2011 and Taylor signed a new three-and-a-half year contract in south Wales in December 2012.
He made his return from his broken ankle, after seven months out, in defeat to Chelsea at Stamford Bridge in April last year before featuring in the final two games of the season.
He has had to settle for the role of Davies's understudy this campaign, making nine competitive appearances, the last in the famous third-round FA Cup victory over Manchester United at Old Trafford at the beginning of the month.
Taylor has made 16 appearances for Wales.