Zelenskiy told reporters that the two leaders will discuss security guarantees for Ukraine during Sunday's talks and that the 20-point plan under discussion "is about 90 per cent ready".
An "economic agreement" also will be discussed, Zelenskiy said, but that he was unable to confirm "whether anything will be finalised by the end".
The Ukrainian side will also raise "territorial issues," he said.
Zelenskiy said that Ukraine "would like the Europeans to be involved" but doubted whether it would be possible at short notice.
"We must, without doubt, find some format in the near future in which not only Ukraine and the US are present but Europe is represented as well," he said.
The announced meeting is the latest development in an extensive US-led diplomatic push to end the nearly four-year Russia-Ukraine war but efforts have run into sharply conflicting demands by Russia and Ukraine.
Zelenskiy's comments came after he said on Thursday that he had a "good conversation" with US special envoy Steve Witkoff and Jared Kushner, Trump's son-in-law.
Kremlin spokesman Dmitry Peskov told reporters on Friday that the Kremlin had already been in contact with US representatives since Russian presidential envoy Kirill Dmitriev recently met with U.S. envoys in Florida.
"It was agreed upon to continue the dialogue," he said.
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.
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
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