The South Korean is currently on a season-long loan on Wearside, but injuries to Jose Canas and Jonathan de Guzman prompted manager Michael Laudrup to look into the possibility of recalling him.
However, despite chairman Huw Jenkins claiming earlier this week that the club had until January 31 to bring Ki back to South Wales, it has now emerged a clause in the agreement dictated that the player could not be recalled beyond the end of December.
"When I was first asked about bringing Ki back (last week), I said I would not because he was doing well at Sunderland and if he came back and didn't play regularly, it would be very difficult for him mentally," said Laudrup.
"But things changed dramatically when we lost Jonathan de Guzman and Jose Canas in the space of a few days.
"The injury to Canas will probably keep him out for about four weeks, and suddenly we only had two midfield players.
"Then I looked into the possibility of bringing Ki back, but the loan agreement said it should have been done by the end of December, so it's not a possibility.
"The only way we can change that is if Ki and both clubs all agree to end the loan, but of course Sunderland are not going to do that.
"It's a difficult position because if players are playing somewhere else, their clubs say they cannot go. Finding players who are not playing is not easy."
Laudrup has also expressed a reluctance to allow left-back Neil Taylor to leave the club, but understands the player's frustration at a lack of first-team opportunities, with Ben Davies favoured in the position.
"I understand if he is frustrated," the Dane continued. "He is a special case because he was a regular here and with the national side, had a serious injury and, when he comes back, a younger player has taken his position.
"But he is a great professional. He has played his games but of course wants to play more.
"We spoke in the summer about things. He wanted to know about the situation and I told him how it was. We have two left-backs and we have at least have 20 games, hopefully more, to play in less than four months.
"So we cannot let go of anyone and that goes for Neil.
"It may be a different situation in summer but, as things stand right now, it's not possible for him to leave."
Swansea City host Tottenham in the Premier League on Sunday.
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