The South Korea international moved to the Stadium of Light over the summer, with former Black Cats boss Paolo Di Canio striking a season-long agreement with Swansea City.
The Swans were quick to point out at the time that they were not turning their back on Ki and still considered him to be part of their future.
The terms of his loan are not believed to include a release clause which could be triggered by Sunderland.
Poyet has, however, been impressed by what he has seen from the former Celtic man and would welcome the opportunity to keep him on Wearside.
He said in the Northern Echo: "It is still early doors and I don't know how expensive he is. But we will see. He plays the type of football that I really admire.
"He has the ability to pass the ball with just one touch and change from one side to the other, or run with the ball and have a shot with either foot.
"If he believes that he can do a bit of the work the other way, the defensive way, he is a player who can give us the lot."
Ki, who cost Swansea £6million in the summer of 2012, has made the holding midfield role his own at Sunderland over recent weeks.
Lee Cattermole has paid the price for a costly dismissal and a subsequent ban, and he may struggle to earn an instant recall after serving the final game of his suspension during a trip to Stoke City on Saturday.
Poyet added: "He (Ki) had to wait for his chance. In the beginning, it was Lee Cattermole in there and he wanted to play in that position.
"Then there was the sending off, and he needed to come in and show the manager that he wanted the shirt. He had to make it difficult for Lee to come back. He is there at the moment, and he has the chance to stay there."