A Ukrainian source said Zelenskiy was interested in travelling to the United States but his team was waiting for official confirmation of Trump's schedule from the White House.
The source added that Ukrainians and US officials had been discussing a proposal for an air ceasefire to take to Russian officials, as part of a new round of peace proposals to try to end the war that began in 2022 with Russia's invasion of Ukraine.
The source said Ukraine had approached Russian President Vladimir Putin in the past with offers of a ceasefire, which had been turned down.
However, some officials believe that pressure on Russia's economy from ongoing Ukrainian drone and missile strikes may soften Putin's stance.
Zelenskiy spoke on Wednesday with US envoys Steve Witkoff and Jared Kushner about the prospects for renewed peace talks with Russia, and said that Ukrainian and US officials could meet in the United States on Tuesday.
Acting Ukrainian Defence Minister Yevhenii Khmara, writing on Telegram, said he and new Commander-in-Chief Mykhailo Drapatyi had met US Ambassador to NATO Matthew Whitaker on Friday in Kyiv and discussed different factors in confronting Russia on the battlefield.
"We have a strong synergy and shared vision of the war with Commander Drapatyi: technological superiority, asymmetric solutions, and more opportunities to destroy the enemy," Khmara said.
"We informed our partners about the situation on the front and Ukraine's steps to force Russia into a fair peace."
A memorial service for the Republican will be held on Tuesday in Washington, where Trump will make remarks ahead of a funeral in Graham's home state of South Carolina on Wednesday.
Graham was a major supporter of Ukraine, travelling there 10 times since the Russian invasion. He pushed for sanctions on Russia as well as US backing for Kyiv.
Meanwhile, Zelenskiy said in an interview broadcast on Friday that co-operation between Kyiv and Washington on drones would include a US factory to produce the unmanned aerial vehicles using Ukraine's advanced technology.
Zelenskiy, interviewed by US right-wing blogger Laura Loomer, said Ukraine wanted to build quickly on an initial agreement on drones clinched with Washington.
Zelenskiy said drone technology was undergoing constant change, with Ukrainian drones now able to operate over 3000km with the prospect of even longer distances.
Ukraine has excelled at drone innovation as it has pursued asymmetrical warfare against Russia during their four-year-old conflict, and Kyiv has shared its advances with some allies.
"Important technology. This is what we have. And America has great technology. Our drone deal is win-win," Zelenskiy said in the interview made available on X.
"We will build a great factory in the United States. We want to (have) lines of production," he said.
Six Ukrainian companies have received permission to export about 100 drones each, the source said, speaking on condition of anonymity.
Other media outlets in Ukraine reported that the two sides had signed a statement of intent that lays the groundwork for a partnership on joint production.
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