But Khalilzad's public statement that the Taliban believe they will "not win militarily" angered senior members of the group, who warned USA officials against mixed messages that could muddle the peace process.
Seventeen years after the US -led invasion that ended Taliban rule, the militants control almost half of Afghanistan and carry out near-daily attacks on local security forces and government officials.
"Without going into detail here, we do believe the Taliban know that at some point they do have to reconcile", he said.
Khalilzad, while speaking to the journalist on Sunday, after the completion of the second round of the Afghan peace talks said that he is "cautiously optimistic" and "hopeful" about the peace talks with Taliban. U.S. officials could not immediately be reached for comment as the State Department has refused to comment on reported talks with the Taliban.More news: India vs Australia: Australian bowlers reveal plans to counter Rohit Sharma
"Its natural, they (the Taliban) will be interested to be part of the system, but when and how and through which method, these are all the items which can be discussed once talks have started with them", said Saleem.
Zalmay Khalilzad, in Kabul to lead talks between the United States, the Taliban and the Afghan government, told reporters he hopes "a peace deal is reached before April 20 next year", when Afghanistan is planning to hold a presidential election. The Taliban have long refused USA demands to negotiate with the Western-backed government in Kabul, which the rebels view as a puppet regime.
The effort has intensified since Zalmay Khalilzad, a former US ambassador to Kabul, was appointed a special USA envoy to Afghanistan in September.
Khalilzad returned to Kabul on Sunday after spending three days in Qatar for discussions with the Taliban's political office representatives there.More news: Apple's New iPad Pro Sparks Another Bendgate After Folding Under Minimal Pressure
The individual, who also spoke on condition of anonymity because of the sensitivity of the talks, said Khalilzad wants to reach a settlement within six months, a timescale the Taliban said was too short.
Khairkhwa and Fazl were among five senior Taliban members released from the US military detention facility at Guantanamo Bay, Cuba in 2014 in exchange for a captured USA soldier, Bowe Bergdahl.
But that strategy has had little, if any, effect on the ground, with the Taliban keeping up a steady tempo of attacks and an affiliate of the Islamic State of Iraq and the Levant (ISIL, also known as ISIS) group carrying out massive bombings targeting the country's Shia minority.More news: Hundreds searching rubble in California for wildfire bodies as rain looms