The MEE report said the draft deal in this regard will be finalised after the US troops withdrawal from the airport is completed by the next week.
Turkish President Recep Tayyip Erdogan’s, who is expected to hold consultations on the matter with his Nato allies mainly the US, will give the final approval to the deal with the Taliban.
However, both sides have now cut a draft deal that could resolve the issue.
According to the main points of the draft agreement, Turkey will recognise the Taliban as the legitimate government of Afghanistan.
Moreover, Turkey and Qatar will operate the airport in a consortium and Ankara providing security through a private firm, whose staff will consist of former Turkish soldiers and police.
Turkish special forces, operating in plainclothes to secure Turkish technical staff but cannot leave the airport perimeter.
One outstanding issue in the way of the deal is that the former Afghan government had already awarded a contract for the airport last October to a United Arab Emirates-based consortium.
The Taliban will need to cut a separate deal with them.
Earlier, an official told Reuters that Turkey will not help run Kabul airport after Nato’s withdrawal unless the Taliban agree to a Turkish security presence as deadly attacks outside the airport highlighted the perils of any such mission.
The Taliban have asked Turkey for technical help to run the airport after next Tuesday’s deadline for all foreign military forces to pull out of Afghanistan, an ultimatum they say applies equally to Turkish troops.
Turkey, which is part of the Nato mission, has been responsible for security at the airport for the last six years.
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.
On Thursday, just days before the military withdrawal deadline and as countries were still racing to evacuate civilians, at least one Islamic State suicide bomber killed 85 people, including 13 US soldiers, outside the airport gates.
One senior Turkish official said the attack raised doubts about the Taliban’s ability to secure the airport or to keep any Turkish operational staff safe.
“The operation can be done by Turkey technically … but our demand is that security should be ensured by Turkey too, through an extensive security team made up of former soldiers, former police, or a fully private firm,” said the official, who spoke on condition of anonymity.
“We have not been keen on Turkey operating the airport in an atmosphere where security is provided by the Taliban, and the attacks yesterday showed this was correct.”