The State Department said late Friday that Pompeo will meet separately in the Qatari capital Doha with Afghan and Taliban teams to the talks.
Pompeo will also see Qatar's ruler, Emir Sheikh Tamim bin Hamad Al-Thani, and the foreign minister on his stop to Doha, the Taliban's base for diplomacy both with the Kabul government and earlier the United States, the State Department said on its public schedule.
The outgoing top US diplomat is on a seven-nation tour of Europe and the Middle East as President Donald Trump shores up late-term priorities.
Earlier in the week, the Pentagon said it would soon pull some 2,000 troops out of Afghanistan, speeding up the timeline established in a February agreement between the United States and the Taliban that envisions a full US withdrawal in mid-2021.
Trump has repeatedly vowed to end "forever wars," including in Afghanistan, America's longest-ever conflict that began with an invasion to dislodge the Taliban following the September 11, 2001 attacks.
President-elect Joe Biden, in a rare point of agreement with Trump, also advocates winding down the Afghanistan war although analysts believe he will not be as wedded to a quick timetable.
The Taliban for the first time is speaking to Afghanistan's government, which under heavy US pressure released militants to meet the insurgents' conditions.
The talks had shown little sign of progress but several sources told AFP on Friday that the two sides appear to have resolved a key sticking point on the rules of the negotiations.
The Taliban, who are Sunni hardliners, have been insisting on adherence to the Hanafi school of Sunni Islamic jurisprudence, but government negotiators said this could be used to discriminate against Hazaras, who are predominantly Shiite, and other minorities.