The 24-year-old signed a season-long loan at Sunderland in August, but Swansea City had the option to recall him mid-campaign if he impressed.
Swansea decided not to ask him to return to the Welsh club, though, despite the South Korea international playing a big role in Sunderland's revival under Poyet.
"There is a chance (of a full transfer)," Poyet said.
"Swansea had an opportunity to call him back, and they didn't. That was a difficult day for me because I was waiting and waiting.
"I think there are a couple of things we need to make sure: where we are and where we want to go, and with the player as well.
"I can see that he's enjoying his football and making a difference."
"He's very happy, it means so much for him to score that goal," he added.
"He cares and he's enjoying his new position a bit further up the pitch and making a difference. I want players with that mentality, to make us play, and he's been excellent.
"He's been the most consistent player for me, in my way of playing."
