Zalmay Mamozy Khalilzad is a US diplomat and the Special Representative for Afghanistan Reconciliation at the Department of State.
He said he was on His Way to Kabul to consult Afghan government officials.
The Taliban also said progress had been made in the negotiations.
However, a spokesman added That talks about "unsolved matters" would continue.
The Taliban have so far refused to hold direct talks with Afghan officials, whom they dismiss as "puppets".
They say they will only begin negotiations with the government once a firm date for the withdrawal of US troops has been agreed.
They envisaged foreign forces withdrawing within 18 months of The Deal being signed In Return for assurances That al-Qaeda and the Islamic State (IS) group would not be allowed to use Afghanistan as a base to attack the US.
The Taliban 's power and reach have surged since foreign combat troops left Afghanistan in 2014.
On Friday, Afghan President Ashraf Ghani said since he became leader in 2014.
Analysis by Secunder Kermani, BBC Afghanistan correspondent
It seems there has been progress in discussions about the Taliban 's key demand - American troop withdrawal - though no timetable has yet been given. In Return , the Taliban appear to be willing to give guarantees about not allowing Afghanistan to become a base for international jihadists.
However, this is a position The Group has articulated for some time now, and it remains to be seen what other concessions they might be willing to make. The Key question for many ordinary Afghans is whether a ceasefire might be on the horizon? That would provide much needed relief to A War weary population.
At the moment the focus is on ending the violence - and getting the Taliban face-to-face with The Afghan government. But it's after That That even more delicate negotiations may have to take place - about The Role of women's rights, freedom of The Press and democracy in Afghanistan.Zalmay Khalilzad is the US special representative for Afghanistan reconciliation Taliban ? Taliban fighters
The militants ruled Afghanistan from 1996 to 2001, imposing a brutal version of Sharia law That included public executions and amputations, and the banning of women from public life.
They were driven from power by US-led troops following the 9/11 attacks which Washington blamed on al-Qaeda militants sheltered by the Taliban .