The deal is at the heart of Ukraine's push to win over Trump's support - including security guarantees - as the US president strives to clinch a rapid end to the war with Russia.
The Ukrainian government was poised to approve the text of the agreement later on Wednesday, so that it could be signed by both sides, the prime minister said, with Zelenskiy set to visit Washington DC on Friday for talks with the US leader.
"This deal could be a great success or it could pass quietly. And the big success depends on our conversation with President Trump," Zelenskiy told a news conference.
Zelenskiy said both sides were still working on organising his potential visit on Friday to sign the deal after a tumultuous week in which the two leaders have exchanged hostile remarks, including Trump calling Zelenskiy a dictator.
The Ukrainian president said success would depend on the United States providing guarantees to protect the future security of Ukraine in the event of any Russian aggression after a peace deal is reached.
A copy of the agreement seen by Reuters on Wednesday and dated February 25 did not spell out concrete security guarantees under the deal but mentions Ukraine's efforts to obtain them.
"The Government of the United States of America supports Ukraine's efforts to obtain security guarantees needed to establish lasting peace," it said.
Trump said during a cabinet meeting at the White House on Wednesday that Zelenskiy will be coming to Washington DC on Friday to sign an agreement on rare earth minerals and other topics.
The deal is part of a broader effort to end the war with Russia and will lay the groundwork for long-term co-operation between Ukraine and the US, Ukrainian Deputy Prime Minister Olha Stefanishyna told Reuters.
"This agreement signifies our commitment to lasting peace and strong partnership, as well as the US desire to participate in Ukraine's reconstruction," she said in a written statement.
Under the wording of the agreement titled "Bilateral Agreement Establishing Terms and Conditions for a Reconstruction Investment Fund," Ukraine would contribute 50 per cent of "all revenues earned from the future monetisation of all relevant Ukrainian Government-owned natural resource assets".
Zelenskiy said the exact amounts and investments would be spelled out in a further agreement to set up the fund.
Those proceeds would go into a fund jointly owned and managed by the United States and Ukraine, the wording of the agreement seen by Reuters says.
The agreement does not name the assets in question but says they would include deposits of minerals, oil, natural gas and other extractable materials as well as other infrastructure such as LNG terminals and ports.
The list would be determined in a future agreement on the fund, while the document does not spell out exactly how much money would be generated for the United States or over what time frame.
In a comment aimed at calming the fears of worried Ukrainians, Prime Minister Denys Shmyhal said Ukraine would never "sign or consider ... a colonial treaty that did not take into account the interests of the state".
The Ukrainian military said on Wednesday it had attacked Russia's Tuapse oil refinery on the Black Sea coast and that at least 40 explosions had been recorded at the site.
Tuapse is home to one of Russia's biggest oil refineries, which has been targeted by Ukrainian drones several times before.
The Ukrainian military also said it had attacked two military airfields in Russia-controlled Crimea but gave no further details on any of the attacks.
Earlier, Russian authorities said they had downed 83 Ukrainian drones overnight over its southern Krasnodar region, including the port of Tuapse, adding that some houses there had been damaged although it made no reference to the oil refinery.
Krasnodar Governor Veniamin Kondratyev said in a post on the Telegram messaging app that three residential houses had been damaged across the region but there were no immediate reports of injuries.
Russia's aviation watchdog Rosaviatsia said on Telegram that the international airport at Sochi, 150km southeast of Tuapse, had been briefly closed to air traffic to ensure air safety.
The Russian Defence Ministry said in a statement that a total of 128 Ukrainian drones had been downed over Russian territory overnight.
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