The Dutch defender was drafted in at the Liberty Stadium in September 2012 on a deal until the end of the season.
The 27-year-old settled quickly in England and saw a number of impressive Premier League displays earn him senior international recognition.
Understandably, Swansea boss Michael Laudrup was keen to tie Tiendalli down on a more permanent contract this summer.
Talks have, however, broken down and he is now exploring other options.
Tiendalli's agent Sebastien Casenaz told talkSPORT: "We have not reached an agreement with Swansea.
"Dwight has been very good this season and the caps he earned with the Dutch national team came as a reward for his performances on the pitch with Swansea.
"As a free agent, of course Dwight is attracting interest from clubs in England and Germany. Currently, discussions continue."