Zelenskiy, speaking after a phone conversation with Trump, said three-sided talks with Russia and the United States would take place in early March.
US negotiators Steve Witkoff and Jared Kushner also took part in the phone call.
"We expect this meeting to create an opportunity to move talks to the leaders' level. President Trump supports this sequence of steps," Zelenskiy wrote on social media platform X.
"This is the only way to resolve all the complex and sensitive issues and finally end the war."
The telephone call took place on the eve of another meeting, between just Ukrainian and US negotiators, to discuss post-war reconstruction.
Zelenskiy said the two leaders discussed both meetings. He thanked the United States for its "active involvement" in the peace process and for missiles for air defence systems that were helping Ukraine endure winter-time attacks.
Addressing a news conference in Kyiv earlier alongside Norwegian Prime Minister Jonas Gahr Stoere, Zelenskiy said Thursday's meeting would include discussion of a "prosperity package".
Zelenskiy said the US wanted to find a way to end as soon as possible Europe's biggest conflict since World War II. But Moscow and Kyiv remain far apart in their positions.
"In my opinion, the difficulties are not at the military level right now. The problem lies in the political will to end this war and in the issue of territories," Zelenskiy said.
"I think that trilateral talks will be held in early March. Tomorrow, economic documents will be prepared at a bilateral meeting between Ukraine and the United States."
Zelenskiy also said Russian claims on Tuesday that Kyiv was trying to obtain nuclear weapons were an attempt to exert political pressure on Ukraine during the talks.
He reiterated Ukraine had no nuclear weapons and called on the US to react to what he described as dangerous Russian rhetoric.
Rustem Umerov, the secretary of the National Security and Defence Council and head of Ukraine's negotiating team will meet in Geneva on Thursday with special envoy Witkoff and Kushner, Trump's son-in-law.
Russia's TASS news agency, quoting a diplomatic source, said President Vladimir Putin's envoy Kirill Dmitriev would be flying to Geneva on Thursday to meet US negotiators, but gave no further details. There was no official Russian comment.
Proceeding with the reconstruction of Ukraine after the destruction wrought by Russian aerial strikes and frontline combat has become a major element in broader talks on how to end the war, which entered its fifth year this week.
Kyiv hopes to attract about $US800 billion ($A1.1 trillion) of public and private funds over the next 10 years to rebuild the nation.
The latest assessment from the World Bank released on Monday showed rebuilding Ukraine's economy will cost an estimated $US588 billion ($A826 billion).
Zelenskiy said Ukrainian and US negotiators would also discuss on Thursday the details of prisoner-of-war exchanges between Ukraine and Russia.
Ukrainian and Russian negotiators met last week in Geneva for their third US-mediated meeting so far this year, but reached no breakthroughs on points including territory.
