A spokesman for the Taliban did not confirm that the planned release, but the South Korean source said that it will possibly happen today or tomorrow.
"The Taliban in return for this exchange have demanded a reconfirmation that all South Korean troops will be out of Afghanistan by the end of the year. The South Korean president has already reaffirmed this," Dan Nolan said.
However, Qari Yusuf Bashir, head of the Taliban's negotiation team in the Afghan city of Ghazni, said they were sticking to their original demand to have 21 Taliban prisoners released from Afghan jails in exchange for the hostages.
Bashir claimed that Kabul will meet their demands and that the Korean and Afghan sides had already approved an initial "prisoners exchange".
Speaking outside the Afghan Red Cross office where the second day of talks were held, Bashir said: "We have great hope that the hostage crisis will resolved today or tomorrow inshallah [God willing]."
The meeting between the Taliban leaders and four Korean officials, which began on Friday, was the direct meeting since the South Korean volunteers were kidnapped.
Qari Yousef Ahmadi, a Taliban spokesman, told Al Jazeera that its officials had received a written guarantee from the Afghan government that they would not be arrested at the meeting.
The meeting comes after days of stalled negotiations on the safe release of the hostages.
Twenty-three South Koreans, who were working with a church group as health aid volunteers, were abducted on July 19 as they travelled by bus from Kabul to the southern city of Kandahar.
Two male hostages have been executed by the Taliban since then.
South Korea's government has since called for aid organisations to leave Afghanistan by the end of the month, citing safety reasons, an embassy official told the Associated Press.
Ahmadi said the departure of South Korean aid workers would move forward negotiations with the Taliban.
Source: Al Jazeera and agencies