Celtic have so far rejected any bids for their South Korean midfielder with Russian club Rubin Kazan previously slapping in an offer of £6m which fell by the wayside.
It is suggested that the Hoops want closer to £8m for Ki, who is also attracting interest from Arsenal and QPR, but talks with Swansea are believed to be at an advanced stage.
Furthermore, Celtic assistant Johan Mjallby has confirmed the 23-year old is looking for the exit door at Parkhead.
"He is keen to move on and the club is in discussion with another club so we have to wait and see what happens. I can't say who the club is," said the Swede.
"There have been a few clubs interested in him but I know for sure there has been one bid for him and I think maybe one or two other bids.
"He is a quality player but on the other hand he is keen to move on so the club needs to do something.
"He was away at the Olympics for a period of time but we will be sorry to see him go."