The 23-year old South Korea international has been linked with the Welsh club in the last few days and it has been revealed that the Swans and Hoops have now come to an agreement on a fee in the region of £5million.
Swans chairman Huw Jenkins confirmed that advanced talks with a club were taking place with Ki now set to agree personal terms and pass a medical before his move is finalised.
"We have agreed a fee with Celtic for Ki. We are currently holding discussion with player and agent over personal terms," he told STV.
"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."