It is understood the flights are expected to depart from Kabul on Thursday to allow people left behind after the August 31 deadline to get out of the war-ravaged country.
The US official told Reuters news agency, on the condition of anonymity, that the new Taliban government agreed to their evacuation after having their hand forced by US Special Representative Zalmay Khalilzad.
However, the official did not confirm whether the people given permission to leave are among those stranded for days in Mazar-e-Sharif.
About 2,000 Afghans are still stuck in the northern city after four charter aircrafts were not allowed to leave the airport.
ITV News Correspondent Romilly Weeks spoke to two British men on Monday who say they have been "abandoned" by the UK government
The Taliban say they are trying to find out who among the stranded have valid travel documents before the flights can leave.
US secretary of state Antony Blinken said in Qatar on Tuesday the Taliban had given assurances of safe passage for all those seeking to leave Afghanistan with proper travel documents. He vowed the US would hold the Taliban to that pledge.
Today's departures will be among the first international flights given the green light by the Taliban to take off from Kabul since their violent seize of the capital, triggering a chaotic US-led mass evacuation of 124,000 foreign nationals and the most at-risk Afghans.
More than a week after Western forces left Afghanistan, the US and UK have been scrambling to find a way to help those desperate to flee the country who remain stranded.
At least a dozen British citizens stuck in the country told ITV News how they fear for their lives, with two business owners saying they feel "abandoned" by the UK government.
Meanwhile, a man desperate to help his family escape was "laughed at" on the phone when trying to contact the government for help, claimed MP Emma Lewell-Buck.
When questioned on her constituent's situation, Boris Johnson responded: "Operation Warm Welcome continues and, as I speak to you, we have already received more than 15,000 people from the Kabul airlift, the biggest exercise this country has undertaken."
The latest flights come after the Taliban this week announced an interim government led by Mullah Mohammad Hassan Akhund, who headed up the Islamist militia in Kabul during the last years of its rule before it retreated in 2001.Other senior posts were given to a militant who is on the FBI's most-wanted list, along with Taliban members who dominated the decades-long war against the US-led coalition and its Afghan government allies.
Despite international pressure to appoint non-Taliban members for a more moderate ruling of the country, it appears all ministers are linked to the militia.
Senior members had previously vowed to rule the country with a softer, more modern approach - but in less than a space of a week, the group have used heavy-handed tactics to break up demonstrations in the capital.