Trump has repeatedly stated that the White House has run out of patience with North Korean leader Kim Jong-un.
According to the source, the talks are being held between Ambassador Joseph Yun, the US special representative for North Korea policy, and Pak Song Il, a senior North Korean diplomat at the country's United Nations mission, using what's known as the "New York channel", which has been an avenue of communication between the USA and North Korea throughout the years.
"Well, it depends on the nature of the threat, right?" he said on ABC's "This Week".
Still, he said the United States is edging closer to war with Kim because of his nuclear provocations. The general is also scheduled to visit China and Japan. I mean, his rhetoric might make Kim Jong Un think that he needs to strike first.
Last week Trump vowed to rain down "fire and fury" on the Hermit Kingdom if Kim continues to threaten to strike the U.S. or its allies with nuclear weapons after the United Nations Security Council imposed strict economic sanctions against the country.
Since the Clinton administration in the early 1990s, the USA has reacted to Pyongyang's "nuclear blackmail" with negotiated agreements that lead to aid and an easing of sanctions followed invariably by broken promises, a growing nuclear arsenal and more threats.
The chairman of Korea's Joint Chiefs of Staff, the deputy commander of R.O.K-U.S.
McMaster also said while poised militarily, the USA is exploring other avenues to confront the threat from Kim's weapons program. But Mattis said Thursday that the American effort was "diplomatically led". Beijing is North Korea's biggest economic partner and source of aid.
"There's nothing imminent today", he said on "Fox News Sunday".
"He conducted two in July, so it wouldn't surprise me if there was another missile test".
The Trump-Xi phone call came as Japan set up a missile-defense system in western areas of the country, following a threat by North Korea to fire missiles over Japan toward the USA territory of Guam.
Yun Sun, a senior associate at the Washington, D.C. -based Stimson Center, argued North Korea would not need intercontinental ballistic missiles to strike South Korea, whose capital sits just 35 miles from the border.