Taliban spokesman Suhail Shaheen said on Wednesday that the group was close to reaching an agreement with the United States.
Shaheen said that negotiations with the US team would continue on Wednesday and they would soon have “good news” for Afghans.
Meanwhile, the BBC reported on Wednesday that the sides had finalized the text of their agreement.
It said that the sides were checking English, Dari and Pashto versions of the deal.
The report said that US negotiator Zalmay Khalilzad would travel to Kabul on Wednesday and would possibly return to the venue of talks.
US and Taliban have held seven rounds of talks over the past one year.
Intra-Afghan negotiations are expected to begin following a deal between Washington and Taliban.