James Bays, Al Jazeera's correspondent in Afghanistan, said: "International forces, not Nato ... are in the area, but I don't think a rescue mission has been ordered."
Earlier the Taliban had threatened to kill all of the hostages if Afghan troops attempted to free them by force.
Negotiations for the hostages' release were under way on Sunday.
Bays reported that the Taliban had extended the deadline as a gesture of good faith to a high-level South Korean delegation that arrived in Afghanistan earlier to negotiate.
He also said the Taliban had extended the deadline as they hoped the people of South Korea would put pressure on their government and that the South Korean government would in turn pressure the Afghan authorities to give in to the Taliban's demands.
The Taliban has demanded the immediate withdrawal of German and Korean troops from Afghanistan and the release of 23 of its members in Afghan prisons.
Roh Moo-hyun, South Korea's president, said on Saturday that Seoul was ready to make efforts for an early release of its citizens and that the Taliban "should send our people home quickly and safely".
South Korea had also reiterated its plans to withdraw its troops by the end of the year, as scheduled.