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."
PREMIER LEAGUE FIXTURES ...
Saturday November 23
12:45 Everton v Liverpool
15:00 Arsenal v Southampton
15:00 Fulham v Swansea City
15:00 Hull City v Crystal Palace
15:00 Newcastle United v Norwich City
15:00 Stoke City v Sunderland
17:30 West Ham United v Chelsea
Sunday November 24
13:30 Manchester City v Tottenham
16:00 Cardiff City v Man Utd
Monday November 25
20:00 West Brom v Aston Villa
Sunderland Fixtures
Saturday November 23
15:00 Premier League Stoke City v Sunderland
Saturday November 30
15:00 Premier League Aston Villa v Sunderland
Wednesday December 4
19:45 Premier League Sunderland v Chelsea
Saturday December 7
17:30 Premier League Sunderland v Tottenham
Saturday December 14
15:00 Premier League West Ham United v Sunderland
Tuesday December 17
19:45 League Cup - Qtr Sunderland v Chelsea
Saturday December 21
15:00 Premier League Sunderland v Norwich City
Thursday December 26
15:00 Premier League Everton v Sunderland
Saturday December 28
17:30 Premier League Cardiff City v Sunderland