Ankara and Doha have agreed on a security framework for the airport mission, but talks on other aspects such as financing are continuing, say Turkish diplomatic sources.
Turkiye and Qatar have reached an agreement on ensuring security at Kabul's main airport should they be awarded the mission amid ongoing talks with the Taliban government.
Turkish diplomatic sources told Reuters on Thursday that Ankara and Doha had agreed on a security framework for the airport mission, but added talks continued on other aspects such as financing.
"It is expected for the Taliban to ensure security outside, and for whoever runs the airport to ensure it inside," one of the sources said.
"The process is continuing constructively," the person said on condition of anonymity.
They added that a delegation of Turkish and Qatari officials were holding talks on the issue in Kabul this week.
Qatar's state news agency said the Taliban government will be in Doha next week to "complete" discussions with Qatar and Turkiye over the operation and management of the airport.
It added in a statement on Thursday that delegations from Qatar and Turkiye have held two days of "intense negotiations" in Kabul this week over control of the airport.
Key air link
Kabul's international airport is landlocked Afghanistan's main air link to the world.
Following the August takeover of Afghanistan by the Taliban, Turkiye has said it would be open to operating it with Qatar but only if its security demands are met.
Reuters has reported that the United Arab Emirates also held talks with the Taliban to keep the airport operational.
Afghans and foreign nationals fled the country through the facility when the Taliban took power in August following two decades of war.
But many are still seeking to flee the nation which is facing the threat of winter food shortages and economic collapse.