A source familiar with the contents of the draft agreement said it did not specify any US security guarantees or continued flow of weapons but says that the United States wants Ukraine to be "free, sovereign and secure".
One of the sources familiar with the deal said future weapons shipments were still being discussed between Washington and Kyiv.
Trump told reporters that Ukrainian President Volodymyr Zelenskiy wanted to come to Washington on Friday to sign a "very big deal".
This came after the two leaders exchanged hostile words last week.
The US president, who has cast the deal as a repayment for billions of dollars in aid to Kyiv, also said some form of peacekeeping troops were needed in Ukraine if an agreement to end the conflict was struck.
Moscow, which launched an invasion of Ukraine three years ago, has refused to accept any deployment of NATO forces.
Some European countries have said they would be willing to send peacekeeping forces to Ukraine.
Trump said on Monday that Moscow would accept such peacekeepers, but the Kremlin denied that on Tuesday.
Trump's rush to impose an end to Russia's war in Ukraine and his lurch toward Moscow has stoked fears of far-reaching US concessions to Russian President Vladimir Putin that could undermine security in Ukraine and Europe and alter the geopolitical landscape.
Trump last week falsely called Zelenskiy an unpopular "dictator" who needed to cut a quick peace deal or lose his country, and falsely accused Kyiv of starting the war.
The Ukrainian leader said the US president was living in a "disinformation bubble".
The deal could open up Ukraine's vast mineral wealth to the US.
"What we're doing is now we're saying, look, we want to be secured," Trump said.
"The American taxpayer now is going to get their money back, plus."
Zelenskiy refused to sign an earlier draft of a minerals agreement as Washington sought rights to $US500 billion ($A787 billion) in Ukraine's natural wealth.
Kyiv protested it had received far less than that in US aid and the deal lacked the security guarantees Ukraine needs.
Under the terms of a draft minerals agreement, according to sources, the United States and Ukraine would establish a reconstruction fund to collect and reinvest revenues from Ukrainian sources including minerals, hydrocarbons and other extractable materials.
Ukraine would contribute to the fund 50 per cent of the revenue minus operating expenses and continue until the contributions reach the sum of $US500 billion.
The United States would provide a long-term financial commitment to the development of a "stable and economically prosperous Ukraine".
Asked what Ukraine would get in return for the minerals deal, Trump cited what he said was $US350 billion already provided by the US "and lots of ... military equipment and the right to fight on".
Scott Anderson, a fellow in governance studies at the Brookings Institution, said the minerals deal would look like "a kind of piracy" to much of the world, but it was necessary to get buy-in from Trump and Republican lawmakers.
"They say this gives (Trump) real skin in the game. I think there is real logic to that," Anderson said.
European officials have been left flat-footed by Trump's decisions to hold talks on ending the war in Ukraine with Russia, spurning both Kyiv and Europe, and by his administration's warning that the US was no longer primarily focused on Europe's security.
Ukraine has deposits of 22 of the 34 minerals identified by the European Union as critical, according to Ukrainian data, including industrial and construction materials, ferroalloy, precious and non-ferrous metals, and some rare earth elements.
