The official described as “useful” a meeting with Alice Wells, the US’s top diplomat for South Asia, earlier this week.
He said the meeting was held in the small Middle Eastern country of Qatar, where the Taliban have maintained a political office since 2013.
“The environment was positive and the discussion was useful,” the Taliban official said on condition of anonymity because he was not authorised to speak to the media.
US officials neither confirmed nor denied a meeting took place.
However, Ms Wells was in Doha, the Qatar capital, this week.
In a statement following her return, the State Department said only that Ms Wells had been in Doha, had met with the ruling family and “the United States is exploring all avenues to advance a peace process in close consultation with the Afghan Government”.
Any talks about a future political setup would be between the Taliban and the Afghan Government, the statement said.
The Taliban have long demanded direct talks with Washington, saying it does not want to talk politics with the US but instead meet face to face to discuss Washington’s concerns — particularly its security concerns — about the Taliban and Taliban involvement in Afghanistan’s future.
It also says it wants a time frame for the withdrawal of the roughly 15,000 US and NATO troops still in Afghanistan.
It wasn’t clear when the next meeting would be held or with whom, but the Taliban official who spoke on condition of anonymity was certain one would be held.