Qureshi arrived in Doha after visiting the United States which is believed to be nearing a deal with the Taliban.
The Taliban has said that the draft agreement is ready and is likely to be signed by the end of this month.
The US has not yet to make an official comment on the developments. Afghan government said on Saturday there was no significant progress in US-Taliban talks on ceasefire.
The Taliban have said that they would scale down their attacks, but not declare a ceasefire.
Meanwhile, US Principal Deputy Assistant Secretary of State for South and Central Asian Affairs Alice Wells is expected to arrive in Islamabad on Sunday for a four-day visit.
During the visit, she will meet with senior Pakistani government officials and members of civil society to discuss issues of bilateral and regional concern, including Afghanistan and the Middle East tensions, Pakistani media reported.
Source : Afghan Voice Agency(AVA)