The South Korean midfielder joined the Stadium of Light outfit in a season-long loan deal in August and his since made 11 Premier League appearances for Poyet's charges.
Ki has been one of the standout performers in a Sunderland side that sits bottom of the table, but Poyet admits the former Celtic player's future is out of his control.
"It's not in our hands at the moment," Poyet is quoted as saying by The Northern Echo.
"It's up to Swansea and not up to us."
Poyet has normally employed Ki as a defensive midfielder, but he was utilised in a more attacking role in the club's 0-0 draw with West Ham on Saturday.
And the Uruguayan believes it is a position more suited to Ki's style.
"We had a chat with Ki," he continued. "He prefers to play in front of the back four, but of course you need to work a lot defensively, and he's not that type of player.
"So we said to him that we'd give him a chance to play forward. He can pass the ball, he's not the type of player where the ball is flying over his head, it could be interesting for us if he plays there again, it could be an option for us."
‘Sir Gary Lineker? I don’t know how you comment on that – I’ve never even considered it. I just try to stand up for the things I believe in’ England legend tells FFT why he won’t stop raising humanitarian issues, even if it affects potential honours
'I fell on the floor and shouted for a penalty. Someone pulled me up and said, "Don’t cheat to win penalties". It was Steve McManaman. I never did it again!' Ex-Liverpool forward reveals harsh lesson he learnt from his team-mate on Reds debut
