The Taliban have asked Turkey for technical help to run Kabul airport after the departure of foreign forces, two Turkish officials told Reuters.
The Taliban also insist that Ankara's military also withdraw fully by the end-August deadline.
"The Taliban have made a request for technical support in running Kabul airport," a senior Turkish official said, adding however that the Taliban demand for all Turkish troops to leave would complicate any prospective mission.
The conditional request by the Taliban, who swept back to power in Afghanistan 20 years after they were ousted in a US invasion, leaves Ankara with a difficult decision over whether to accept a hazardous job, one official said.
Mainly Muslim Turkey was part of a NATO mission in Afghanistan and still has hundreds of troops at Kabul airport.
The officials say they are ready to withdraw at short notice.
Another Turkish official said a final decision would be made by the Aug. 31 deadline for foreign forces to leave the country and end a 20-year military involvement in Afghanistan.
However, the Taliban has not yet confirmed the request for technical help from Turkey.
Keeping the airport open after foreign forces hand over control is vital not just for Afghanistan to stay connected to the world but also to maintain aid supplies and operations.
In the meantime, the US military will continue evacuating people from Kabul airport until an Aug. 31 deadline if needed but will prioritize the removal of US troops and military equipment on the last couple of days, the Pentagon said on Wednesday, Reuters reported.
There are about 5,400 troops at the airport, a number that President Joe Biden says is set to go down to zero by the end of the month, depending on cooperation from the Taliban.
Army Major General William Taylor, with the US military's Joint Staff, told a news briefing more than 10,000 people were at Kabul airport waiting to be evacuated from Afghanistan.
He said that in the previous 24 hours, 90 US military and other international flights had evacuated 19,000 more people, bringing the total evacuation number so far to about 88,000.
He said one plane had departed every 39 minutes.
On Thursday, Reuters also reported that the US and allies urged people to move away from Kabul airport due to the threat of a Daesh attack as Western troops hurry to evacuate as many Afghans as possible before an Aug.