The Black Cats manager admitted he will try to tempt the Swansea midfielder into making a full-time move to the north east.
Ki scored one and set up another for hat-trick hero Adam Johnson in Sunderland's impressive 4-1 Premier League romp at Fulham on Saturday.
The victory lifted Poyet's men off the foot of the table, and the Uruguayan said the better Sunderland's form is the more chance he has of convincing Swansea loanee Ki to sign long-term.
"There is a chance (of a full transfer)," said Poyet.
"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."
Ki is on a season-long loan at the Stadium of Light, but Swansea boss Michael Laudrup seriously considered recalling the 24-year-old last week, to ease a midfield injury crisis.
But the Dane decided against it, leaving Poyet as relieved as he was delighted.
"At least we still have him, I was nervous in that time," said the former Uruguay midfielder.
"He's very happy, it means so much for him to score that goal.
"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.
"Then of course John O'Shea and Wes Brown at the back, we're more solid and pressing some of the space.
"The basics are there then hopefully, if we can keep them all fit."