Baradar, who heads the fundamentalists' political bureau, will be accompanied by Mullah Mohammad Yaqoob, son of the late Taliban co-founder Mullah Omar, and Sher Mohammad Abbas Stanekzai in senior positions in the government, the source added.
Haibatullah Akhunzada, the supreme religious leader of the radicals, will focus on religious affairs and governance within the framework of Islam, he added.
The Taliban seized Kabul on August 15 after sweeping through most of the country but face resistance in the Panjshir Valley, north of the Afghan capital, with reports of heavy fighting and casualties.
Amid many uncertainties, the Taliban is all set to form the new Afghan government. As per the latest reports, Taliban’s co-founder Mullah Abdul Ghani Baradar is likely to become the head of the executive council.
Several thousand fighters from regional militias and remnants of the former government's armed forces massed in the rugged valley under the leadership of Ahmad Massoud, son of former mujahideen commander Ahmad Shah Massoud.
The fundamentalists recaptured Afghanistan after the end of the 20-year U.S.-NATO military occupation, which cost two trillion dollars and 3,000 U.S. troops killed.
Many Afghans fear the return of the Taliban regime, whose first period of rule between 1996 and 2001 committed various abuses, especially against women, girls and ethnic minorities.