According to CNN, the talks between the USA and North Korea's intelligence officials are aimed at laying the ground for a meeting between Pompeo and the head of the North's Reconnaissance General Bureau, whose identity has not been confirmed.
That work has been led by Central Intelligence Agency Director Mike Pompeo, Trump's pick to become secretary of State.
The lines of dialogue between North and South Korea were reopened in January for the first time in two years, culminating in the North Koreans attending the Winter Olympics.
Since then, the North Korean leader has reaffirmed his commitment to discussing denuclearization as well as his willingness to hold summit talks with the South Korean and USA presidents.
Although Trump tweeted on March 28 he was looking forward to the meeting, expressing, "there's just a good chance that Kim Jong Un will perform what is ideal for his people and also for humanity", many economists also have expressed doubt about the close program's aims.
The talks will lay the groundwork for a meeting between Mr Pompeo and his North Korea counterpart, who is the head of the Reconnaissance General Bureau.
"The North Koreans are pushing to have the meeting in their capital, Pyongyang", but it is "unclear whether the White House would be willing to hold talks there", CNN said.
"It's a natural step in the right direction".
CNN said that officials from the United States and North Korea have spoken several times and even met in a third country, with the first intention being on deciding a date to hold the talks. The representatives of the United States of America and North Korea have already met in a third country.
They said: "We caution the public to understand that North Korea views its nuclear programme to be sacrosanct and will likely not give it up, no matter what they say during any negotiations".
Speaking at Duke University in North Carolina, Haley said, "When the president ends up speaking with Kim, the conversation has to be about denuclearizing. What we will see next is the exchanges of presidential envoys between the USA and North Korea".
The working-level talks began on Saturday morning at a facility on the North side.