The South Korea international moved to the Stadium of Light on loan last summer after being deemed surplus to requirements by Michael Laudrup at Swansea.
But Laudrup has been sacked, and any new manager will want to assess the players on the books.
Sunderland are eager to wrap up a permanent agreement, but that won't happen now.
Gus Poyet: "We definitely want him to stay."
Ki: "I don't know if I will be playing here next season. I've no idea what will happen in the future, but right now I am happy playing for Sunderland.
"Since Gus Poyet came in, we have improved with and without the ball and are a lot more confident.
"Reaching Wembley and winning the derby were special and I am pleased with how things are going."