Mullah Abdul Ghani Baradar will lead a new Afghan government set to be announced shortly, sources in the Islamist group said on Friday.
The Taliban are battling rebel fighters in the Panjshir Valley and are striving to ward off economic collapse, Tolo News reported.
Baradar, who heads the Taliban's political office, will be joined by Mullah Mohammad Yaqoob, the son of late Taliban co-founder Mullah Omar, and Sher Mohammad Abbas Stanekzai in senior positions, three sources said, the report added.
"All the top leaders have arrived in Kabul, where preparations are in final stages to announce the new government," one Taliban official told a global news wire.
Haibatullah Akhunzada, the Taliban's supreme religious leader, will focus on religious matters and governance within the framework of Islam, another Taliban source said.
The Taliban, which seized Kabul on August 15 after sweeping across most of the country, have faced resistance in the Panjshir Valley, north of the capital, with reports of heavy fighting and casualties.
Several thousand fighters of regional militias and remnants of the government's armed forces have massed in the rugged valley under the leadership of Ahmad Massoud, the son of former Mujahideen commander Ahmad Shah Massoud.
Efforts to negotiate a settlement appear to have broken down, with each side blaming the other for the failure.
The government's legitimacy in the eyes of international donors and investors will be crucial for an economy grappling with drought and the ravages of a conflict that killed an estimated 240,000 Afghans, Tolo News said.