"They say the government has accepted those names and says that those prisoners will be released soon."
Qari Yousuf Ahmadi, a Taliban spokesman, said the new deadline is to allow the government time to get Taliban fighters out of jails and hand them over.
The Afghan government has not confirmed a prisoner deal reached but authorities previously had publically refused to swap prisoners for the hostages.
The deadline extension came as one of the 22 Korean hostages was allowed by the Taliban to give an interview to a local news agency.
The woman, who identified herself as Yo Syun-ju, told an Afghan journalist by telephone that all the hostages were sick and pleaded for help to secure their release.
Yo, who said she was from Seoul, described her situation as "dangerous," and said: "Day by day it is getting very difficult ... We are all sick and we have a lot of problems."
Earlier on Thursday, South Korea dispatched a senior envoy to Afghanistan to aid in negotiating the release of the held Koreans.
The Koreans, including 18 women, had been split into small groups and were being fed bread, yogurt and rice, Ahmadi said.
The Taliban spokesman said Major General Muhammad Munir Mangal, deputy interior minister of Afghanistan, contacted the Taliban and said the government would make a decision regarding their demands by the noon Friday deadline.
"The Taliban are not asking for money, we just want to exchange our prisoners for Korean hostages"
Qari Yousif Ahmadi, Taliban spokesman
Ahmadi said: "The Taliban are not asking for money. We just want to exchange our prisoners for Korean hostages ... When they release, the Taliban we will release the hostages."
Roh Moo-hyun, the South Korean president, spoke with Hamid Karzai, his Afghan counterpart, on Thursday, and they agreed to fully co-operate on freeing the remaining captives, Roh's office said.
But Seoul also said it opposed the launch of a military operation to try to free them.
Ali Shah Ahmadzai, police chief of the Ghazni province where the Koreans were captured, said Afghan negotiators were speaking with the Taliban over the phone in efforts to secure their release.
Ahmadzai said: "We will not use force against the militants to free the hostages ... The best way in this case is dialogue."
Despite calls for negotiation, Afghan police and army units remained mobilised in large in Ghazni' Qarabagh district, where authorities believe the hostages are being held in a number of locations.
On Wednesday, the Taliban killed one of the hostages. Afghan officials confirmed they had recovered the bullet-riddled body of Bae Hyung-Kyu, a Presbyterian pastor and the leader of the South Korean group.
The Taliban claimed responsibility for the killing, accusing the Afghan government and South Korean negotiators of failing to act in good faith after they rejected an initial list of eight Taliban fighters to be freed from prison.
South Korea has condemned the Taliban for the killing of Bae.
Baek Jong-chun, the chief national security adviser, said on Thursday: "The government and the people of South Korea condemn the kidnapping of innocent civilians and the atrocity of harming a human life."
"Harming innocent civilians can never be justified and we will never forgive this kind of inhumane act," he said in a nationally televised statement.
Bae, who was killed on his 42nd birthday, was co-founder of the Saem-Mul church which sent the volunteers to Afghanistan. He had a wife and nine-year-old daughter.