Ki is being chased by several clubs but Premier League outfit Swansea appear to have won the race after chairman Huw Jenkins confirmed they have agreed a fee of around £6 million ($9.4 million, 7.6 million euros).
"We have agreed a fee with Celtic for Ki. We are currently holding discussion with player and agent over personal terms," Jenkins said.
"We are aware of other clubs' interest but we are hopeful we can conclude a deal in the next 24 hours. We feel he is a very exciting young player who has a good career in front of him."
The 23-year-old former FC Seoul star has not returned to Celtic since playing for South Korea at the London Olympics and was absent again on Monday as Neil Lennon's squad flew out for the first leg of their Champions League play-off clash with Helsingborg in Sweden.
Celtic assistant manager Johan Mjallby said: "Ki is not travelling. 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.
"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."
Ki, who helped South Korea win Olympic bronze, played a key role as Celtic won the Scottish title last season and the Scottish Cup in 2011.
Source: AFP
Source: AFP