He played 38 times for Swansea last season - including in their League Cup final victory over Bradford City at Wembley - after joining from Celtic for 5.5 million pounds ($8.51 million)in August 2012.
But Ki has made only three substitute appearances so far this season in the face of competition at Swansea from Jonjo Shelvey, Jose Canas and Jonathan de Guzman.
Sunderland lost 3-1 at Crystal Palace in the league on Saturday and have one point from their first three games.
($1 = 0.6465 British pounds)
(Writing by Steve Wood; Editing by Ken Ferris)
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