If an agreement is sealed, it could revive hopes for a long-term solution to the conflict in Afghanistan.
Taliban and U.S. negotiators met on Wednesday and Thursday to discuss the signing of a peace deal, according to a spokesman for the Taliban office in Qatar. The talks were "useful" and would continue for a few days, the spokesman, Suhail Shaheen, said on Twitter early on Friday.
U.S. President Donald Trump had called off the stop-start talks to end the 18-year war in September after an U.S. soldier was killed in an attack by the militant group.
They resumed but were interrupted again in December after the Taliban launched a suicide attack on a U.S. base outside Kabul killing two civilians.
Two sources close to the matter told Reuters on Wednesday that the Taliban's top leadership had now agreed to implement a 10-day ceasefire with U.S troops once a deal was signed in Doha, and to "reduce" attacks against the Afghan government.
A senior Taliban commander said: "The U.S. wanted us to announce a ceasefire during the peace talks which we had rejected. Our shura (council) has agreed to a ceasefire the day the peace accord is signed."
Once an agreement is in place, the Taliban and Afghan government could meet face to face in Germany, said the commander. Previously, the Taliban had refused to engage in talks with the Afghan government.
The U.S. team in Doha had demanded a ceasefire "which we had declined due to some issues," the Taliban commander said. "Now most of our reservations have been addressed." Another source close to the talks confirmed the commander's version of events.