James Bays, Al Jazeera's correspondent in Afghanistan, said: "They [the Taliban] have extended [the deadline] in the past, but they say they are serious this time."
He reported there was a build up of security forces in the area.
"There are a lot of troops and police in the area near the main highway where the South Koreans were kidnapped."
The leader of the group, Bae Hyung-kyu, a 42-year-old pastor, was shot dead on Wednesday and his bullet-riddled body found in a desert area of the province.
Bae's body arrived in South Korea on Monday.
Melissa Chan, reporting for Al Jazeera from Seoul, said: "The family members have said that they will not hold a funeral until the rest of the hostages are back and safe."
Earlier on Monday, Yousuf had denied that there had been any agreement to extend talks further.
"We are still awaiting the decision of the leadership council. We have not extended the deadline till Wednesday," he told Reuters by telephone from an unknown location.
Reports had said that the Taliban extended their "final" deadline at the request of Afghan mediators, but insisted that the release of Taliban prisoners was the only way to settle the crisis.
The "final deadline" was issued by the movement's leadership council on Sunday and orginally ran out at 0730 GMT.
The Taliban have demanded the withdrawal of South Korean troops from Afghanistan and the return of prisoners held by the Afghan authorities.
On Sunday, Yousuf said that the group's demands remained the same.
He said: "We have the same previous demands; the first is accepting to withdraw the Korean forces from Afghanistan."
"The second demand is still pending as the Afghan government delegation has said that it does not have the authority to release Taliban prisoners."
For their part, Afghanistan's interior ministry and the presidential palace have said a hostage swap is out of the question.
An Afghan team that was supposed to have held more talks with the Taliban on Saturday could not reach the group because of security concerns in Ghazni province, a provincial source said.
The Taliban has said that if anything happens to the South Korean hostages, "the Afghan government and the South Korean government will be responsible".
Source: Al Jazeera and agencies