By Agence France-Presse
They "will discuss making progress on all four pillars of the Singapore Summit joint statement, including achieving the final, fully verified denuclearization," a statement said, referring to the agreement signed at a June summit between President Donald Trump and North Korean leader Kim Jong Un.
The meeting comes with the two sides at loggerheads nearly five months after the summit, in which Trump and Kim pledged to work toward the denuclearization of the Korean peninsula.
North Korea's foreign ministry has warned that Pyongyang will "seriously" consider reviving its nuclear weapons program unless US sanctions are lifted.
In announcing the meeting with Kim Jong Chol on Sunday, Pompeo said he expected to "make some real progress" including on laying the groundwork for a second summit between Trump and Kim Jong Un.
Kim Yong Chol is a general, a former top intelligence chief and right-hand man to the North Korean leader.
He visited the White House in the diplomatic run-up to the Singapore summit, and has been Pompeo's chief interlocutor in the months since.
In mid-October, Pompeo evoked the possibility of a second summit, preceded by talks with Kim Yong Chol.
"We're working on finding dates and times and places that will work for each of the two leaders," Pompeo said at the time.