Russian President Vladimir Putin proposed a May 9 ceasefire to coincide with Victory Day in Russia in a phone call with Trump the previous day, according to the Kremlin.
"We have instructed our representatives to contact the United States president's team and clarify the details of the Russian proposal for a short-term ceasefire," Zelenskiy posted on social media on Thursday.
"We will find out exactly what is being discussed, whether it's a few hours of security for a parade in Moscow or something more."
Zelenskiy said Ukraine was proposing a longer-term ceasefire.
Meanwhile, Russian attacks overnight killed one person in the central Ukrainian city of Dnipro and wounded dozens more in the southern port city of Odesa, as Ukraine continued to strike industrial facilities inside Russian territory for a second day in a row.
In Dnipro, a drone attack killed one person and injured five, Dnipropetrovsk regional head Oleksandr Hanzha said in a post on Telegram.
He said a shop, residential building and vehicles were damaged.
In Odesa, region head Oleh Kiper said Russian forces launched waves of drone attacks on residential buildings and civilian infrastructure in Odesa overnight, wounding 20 people.
He said Ukrainian air defences had downed many of the incoming targets but hits and falling debris damaged residential buildings, a hotel, a kindergarten and an administrative building and caused fires at several locations which were now extinguished.
Russia's Perm region in the Ural mountains, more than 1500km away from Ukraine, reported a drone attack for a second day in a row.
Governor Dmitry Makhonin said an industrial facility was hit, and there were no casualties or any significant damage.
He did not provide further details.
Krasnodar regional governor Veniamin Kondtratyev said a fire caused by a Ukrainian drone attack on the Tuapse oil refinery had been put out after raging for almost two days, with oil products spilling out on the streets of the city.
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