CNN quoted a source familiar with the US-North Korea talks as saying that Kim Yong Chol would be carrying a new letter for Trump.
The North Korea official could arrive in Washington by Thursday, according to CNN.
Experts have said that the United States and North Korea may seek to focus on making some concessions to break the current deadlock. Officials are expecting to announce an exact date and place soon. NPR's Michele Kelemen has this story. But hours before Kim Yong Chol's arrival on Thursday, the US president unveiled a revamped USA missile defence strategy that singled out the country as an ongoing and "extraordinary threat".
A State Department spokesman, Robert Palladino, said they had a "good" discussion toward progress on commitments Mr Trump and Mr Kim Jong Un made at their June summit in Singapore.
"Look, we continue to make progress, we're continuing to have conversations", she told reporters at the White House.
US President Donald Trump will meet up with North Korean leader Kim Jong-un by the end of February.
Kim, backed by ally China as well as South Korea, is also hoping for an easing of worldwide sanctions, but the United States insists on maintaining maximum pressure until Pyongyang moves forward on giving up its nuclear weapons.
While North Korea has refrained from provocations, analysts remain wary of Pyongyang's nuclear program and have said engagement is taking place as weapons production is ongoing. He noted, however, that in order for a second summit to be successful, "the bar will be higher". But it's really a qualified win.
While key nuclear sites have been dismantled, USA intelligence reports said Pyongyang has increased its production of fuel for nuclear weapons. But there hasn't been any concrete progress on denuclearization.
Meanwhile a senior official at Japan's foreign ministry spoke with the USA special representative for the North, Stephen Biegun, by telephone.
In September, Trump called the letters from Kim "beautiful" and said, "We fell in love". And as a result of that, American negotiators have not been able to engage their counterparts at the working level at all.
The prospect of a second summit has always been talked about. The State Department says Biegun is heading to Sweden. (AAP) Mr Pompeo and North Korean leader Kim Jong-un held talks over the weekend. There are big gaps to bridge. The U.S. could, for example seek, the destruction of the Yongbyon nuclear processing site, while allowing some trade between North and South Korea to be exempted from sanctions.
Trump has praised Pyongyang's willingness to turn over remains of American service members who died in the Korean war and the release of three US citizens who were detained in North Korean jails.
At the United Nations on Friday, U.N. Secretary-General Antonio Guterres encouraged both countries to continue talks.
But the agreement they signed was long on rhetoric and short on details, with Kim pledging to work towards the "denuclearisation of the Korean peninsula".
The U.S. and North Korea seemed close to war at points during 2017. All eyes are on Washington.
Kim has at times snubbed US envoys, including Secretary of State Mike Pompeo, evidently preferring to deal directly with Trump. Lee believes the diplomatic window for negotiations won't stay open forever, however, and said the next summit could be a make-or-break moment for Trump's aspirations to hash out a viable deal on denuclearizing North Korea.