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 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."
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