The `Flying Finn` parts ways with the Championship high-flyers having managed just two substitutes appearances in the league this term, both of which came back in August.
He enjoyed a successful three-month loan spell with Derby between September and December, making a total of 12 outings and scoring twice, and a return to Pride Park could be a possible option.
Kuqi signed an 18-month contract with Swansea in January 2010, returning to England on a free transfer from German side TuS Koblenz after a previous eight-year spell in the country which included stints with the likes of Sheffield Wednesday, Ipswich and Crystal Palace.
The 34-year-old played a large role under previous Swans boss Paulo Sousa but has found first-team opportunities limited during Brendan Rodgers` reign.
Rodgers told City`s official website: "Unfortunately it hasn`t worked out for Shefki this season because he hasn`t played as much as he would have liked. However, it goes without saying that he has always conducted himself in a totally professional manner on and off the field. He is a terrific individual and we all wish him well in his next challenge."
Source: PA
Source: PA