Announcing the meeting, Zelenskiy said "a lot can be decided before the New Year," as the United States drives efforts to end Russia's full-scale war in Ukraine.
"As for the sensitive issues: we will discuss both Donbas and the Zaporizhzhia nuclear power plant. We will certainly discuss other issues as well," he told reporters in a WhatsApp chat.
Axios later quoted Zelenskiy as saying he hoped to agree on a peace framework with Trump during the meeting and that he would be willing to bring that framework to a referendum in Ukraine if Russia agrees to a ceasefire.
Russia wants Ukraine to withdraw from the parts of the eastern Donetsk region that Russian troops have failed to occupy during almost four years of war, as it seeks full control of the Donbas, comprising the Donetsk and Luhansk regions.
Ukraine wants fighting to be halted at current battle lines.
The US, seeking a compromise, proposed a free economic zone if Ukrainian forces leave the area.
Territorial issues remain a hurdle to negotiations.
Zelenskiy said on Tuesday that he would be willing to withdraw troops from Ukraine's eastern industrial heartland as part of a plan to end the war if Russia also pulls back and the area becomes a demilitarised zone monitored by international forces.
Any compromises on territory should be decided by the Ukrainian people in a potential referendum, Zelenskiy said on Friday.
The Zaporizhzhia nuclear power plant, Europe's biggest, is located on the front line and is controlled by Russian forces.
Zelenskiy said in his statement on WhatsApp that his meeting with Trump aimed to "refine things" in the drafts and to discuss potential deals on Ukraine's economy.
He added that he was not ready to say if any deal would be signed during his visit but that Ukraine was open to it.
A security guarantee agreement between Ukraine and the US was "almost ready" and the 20-point plan draft "is about 90 per cent" complete, Zelenskiy said.
Wary of failed guarantees from allies in the past, Ukraine is seeking robust and legally binding deals to prevent further Russian aggression.
Trump, who has at times expressed frustration with the slow pace of progress in the negotiations, previously suggested that he would meet with Zelenskiy or Russian President Vladimir Putin if he felt that a major diplomatic advance was possible.
European leaders might join the talks online, according to Zelenskiy.
On Friday, he discussed "significant progress" in the peace efforts with Finnish President Alexander Stubb.
Russian officials have not indicated which peace plan proposals they would be willing to accept.
Russia's Kommersant newspaper reported that Putin told some of Russia's top businessmen that he might be open to swapping some territory controlled by Russian forces elsewhere in Ukraine but that in exchange he wanted the whole of the Donbas.
On the ground, one person was killed and three others were wounded when a guided aerial bomb hit a house in Ukraine's Zaporizhzhia region while six people were wounded in a missile strike on the city of Uman, local officials said on Friday.
Russian drone attacks on the city of Mykolaiv and its suburbs overnight into Friday left part of the city without power.
Energy and port infrastructure were damaged by drones in the city of Odesa on the Black Sea.
Meanwhile, Ukraine said that it struck a major Russian oil refinery on Thursday using UK-supplied Storm Shadow missiles.
Ukraine's General Staff said that its forces hit the Novoshakhtinsk refinery in Russia's Rostov region.
"Multiple explosions were recorded. The target was hit," it wrote on Telegram.
Rostov regional governor Yuri Slyusar said that a firefighter was wounded when extinguishing the fire.
with Reuters
