The US president also declined to provide Tomahawk missiles to Ukraine and mused about giving security guarantees to both Kyiv and Moscow, comments that the Ukrainian delegation found confusing, added the two sources, who requested anonymity.
After his meeting on Friday with Zelenskiy, Trump publicly called for a ceasefire on the current frontlines, a position that the Ukrainian president then embraced in comments to reporters.
A third person said Trump came up with that proposal during the meeting after Zelenskiy said he would not voluntarily cede any territory to Moscow.
Trump underscored that position in remarks to reporters on Sunday.
"We think that what they should do is just stop at the lines where they are, the battle lines," he said on Air Force One.
"The rest is very tough to negotiate if you're going to say, 'you take this, we take that.'"
Asked if he had told Zelenskiy that Ukraine must cede all of the Donbas region to Russia, Trump said no.
"Let it be cut the way it is. It's cut up right now. I think 78 per cent of the land is already taken by Russia," Trump said.
"You leave it the way it is right now. They can ... negotiate something later on down the line," he said.
The meeting was a clear disappointment for Zelenskiy, who had hoped to convince Trump to supply his government with long-range Tomahawk missiles capable of hitting deep inside Russia.
Elements of the talks were first reported by The Financial Times on Sunday.
In recent weeks, there had been indications Trump was deprioritising efforts to force a deal on Kyiv and Moscow, in favour of throwing his full support behind the Ukrainians.
But the Friday meeting indicates that Trump may revert to mediating a deal.
US officials repeatedly brought up the possibility of a territorial swap between Ukraine and Russia - an idea that Trump had embraced earlier in the year - and the US president said a quick agreement was essential, the sources said.
"It was pretty bad," one of the sources said."The message was, 'Your country will freeze, and your country will be destroyed'" if Ukraine doesn't make a deal with Russia.
Trump resorted to profanity several times throughout the meeting, the source said.
Two sources were left with the impression that Trump was influenced by a Thursday call with Russian President Vladimir Putin.
During that call, The Washington Post reported that Putin proposed a territorial swap in which Ukraine would cede the regions of Donetsk and Luhansk in return for small parts of Zaporizhzhia and Kherson.
One of the sources said that US officials proposed precisely that swap to Zelenskiy on Friday.
But Ukrainians see major strategic value in the portion of Donetsk and Luhansk that they still hold - they believe giving up that territory would make the rest of Ukraine much more vulnerable to Russian offensives, the person said.
"We will give nothing to the aggressor, and we will forget nothing," Zelenskiy said during his nightly video address on Sunday. "We clearly see that this Russia is a long-term threat."
On Thursday, before meeting Zelenskiy, Trump said he would soon meet Putin in Budapest.
A Kremlin aide said shortly after that US Secretary of State Marco Rubio and Russian Foreign Minister Sergei Lavrov would speak in the coming days to prepare for the summit.
The White House and the Ukrainian president's office did not respond to a request for comment.
