The talks were confirmed by a Taliban spokesman in an interview with RFE/RL's Radio Free Afghanistan.
The International Committee of the Red Cross in Afghanistan says it has been asked to make a venue available where the two sides can meet.
The Taliban kidnapped 23 South Korean aid workers in Ghazni Province on July 19. They have killed two male captives and released two female hostages.
The Taliban has threatened to kill the hostages unless the Afghan government releases some Taliban prisoners held in Afghan jails.
NATO Convoy Attacked
Meanwhile, three Germans were reportedly killed on the outskirts of Kabul today when an explosion hit a NATO military vehicle.
At least one civilian was also injured in the blast, which Afghan police say was caused by a roadside bomb.
The European Union's foreign-policy chief, Javier Solana, denounced the attack as a "terrorist act."
A spokesman for the NATO-led International Security Assistance Force (ISAF) confirmed an attack on a German Embassy convoy on the outskirts of Kabul, but could not comment on any casualties.
The German Embassy says it is aware of an incident, but also could not comment.
(with material from agency reports)