The South Korea international had been loaned out to Sunderland last season but is back in the fold under Garry Monk and is happy to continue his development in Wales
Ki's future at the Liberty Stadium looked in serious doubt after he was sent on loan to Sunderland for the 2013-14 season but, under new manager Garry Monk, the South Korea international is back in favour.
He scored in the first half of Swansea's surprise 2-1 win at Manchester United on the opening day of the season and played another 90 minutes in the 1-0 triumph over Burnley on Saturday.
Ki told the South Wales Evening Post: "I'm in negotiations. It would be great to stay here.
"I'm very pleased with everyone, the squad and also with every start – which I can learn something from.
"The way we play football is very suitable so I think I can maybe expect to extend my contract."
The 25-year-old revealed that he had offers to go to other clubs in the close-season but is happy to be part of Monk's plans.
"I had a few options to go but I decided to stay because I know these players can help me to be a better player," he added.
"It's easy for me to pass it and easy for me to create chances so I'm very happy to stay here.
"[Wilfried] Bony, [Nathan] Dyer, [Wayne] Routledge, [Bafetimbi] Gomis, Gylfi [Sigurdsson] – these players know how to play football so it's easier for me to play with them."