Trump agreed last month to a landmark summit with the nuclear-armed North but with no specific dates or venue set, there had been questions over Pyongyang's intention to participate, AFP reported.
On Monday, Kim discussed the "the prospect of the DPRK-US dialogue" with party officials, the state KCNA news agency said, referring to the North by its official acronym.
He delivered a report "on the development of the recent situation on the Korean Peninsula", including the separate summit with South Korea to be held later this month, it said.
In a growing rapprochement on the Korean Peninsula, Kim is scheduled to meet South Korea's President Moon Jae-in for a rare inter-Korean summit on April 27.
Trump has also agreed to meet Kim to discuss denuclearization as soon as next month. The summit would be the first between a sitting US president and a North Korean leader.
But the North remained publicly silent for weeks after its leader's invitation to talks was first delivered to Trump by South Korean officials.
This fueled concerns in Washington that Seoul had overstated the North's willingness to negotiate over its own nuclear arsenal, even as officials scrambled to prepare for the prospective meeting.
Kim's remarks break that public silence, although he did not specifically refer to a summit with Trump.
They follow media reports that North Korean officials have privately told their US counterparts Kim is ready to discuss denuclearization.
Trump said Monday he planned to meet Kim in "May or early June".
"I think there will be great respect paid by both parties and hopefully there will be a deal on denuking," he said.
Pyongyang's frenetic diplomatic activity marks a stunning turnaround after a year of high tensions which saw the North carry out nuclear and missile tests, triggering a fiery war of words with Trump.
Kim sent a high-profile delegation to the Winter Games in the South in February, before making his international debut last month with a visit to Beijing – his first overseas trip since taking power in 2011.
North Korea's Foreign Minister Ri Yong Ho arrived in Moscow on Monday after stopping in Beijing. He also paid a visit last month to Sweden, which acts as a diplomatic go-between for Washington and Pyongyang.
If the Kim-Trump summit does take place, many remain skeptical about the whether a meeting between the two unpredictable leaders can succeed.
It is scheduled to take place without the months of groundwork that usually precedes such meetings.
No specifics have yet emerged concerning the date or venue, with a third country such as Mongolia or Sweden reportedly under consideration to host the talks.