The Republican presidential candidate said during a campaign stop in New York last week that he would "probably" talk with Zelenskiy while the Ukrainian leader was in the country for the 79th session of the United Nations General Assembly in New York.
Before his trip, Zelenskiy said he planned to present his "victory plan" to end the war in Ukraine to Trump, Democratic President Joe Biden and Vice President Kamala Harris, the Democratic presidential candidate.
But while Trump's plans can always change, a meeting is at this point extremely unlikely, said the sources, who requested anonymity to discuss private matters.
It was not clear whether the two leaders ever formally set a date for an encounter. But the chances of a meeting went down substantially after Zelenskiy traveled to a munitions factory in Pennsylvania on Sunday alongside the state's Democratic governor, Josh Shapiro, the sources said.
The Trump campaign was upset at the move, those sources said, which they saw as a campaign stop. Shapiro is a close ally of Harris, and Pennsylvania is one of the most politically competitive states in the nation.
On Wednesday, Mike Johnson, the top Republican in the House of Representatives, wrote a letter to Zelenskiy demanding that he fire Ukraine's ambassador to the United States for helping to organize the trip.
Pennsylvania has a substantial number of voters of Eastern European descent - including many Ukrainian-Americans. Both campaigns have been courting them aggressively in the final weeks before the Nov. 5 election.
Even before Zelenskiy's trip to Pennsylvania, some allies had been pushing Trump to avoid meetings with foreign leaders during the final stretch of the race and instead focus solely on campaigning, according to a separate source close to the former president.
Neither the Trump campaign nor the Ukrainian embassy in Washington responded to requests for comment.
Trump has consistently described U.S. aid to Ukraine as a waste of money and has declined to say whether he wants Ukraine to win. While Trump and Zelenskiy talked over the phone in July, they have not talked in person since Trump's 2017-2021 term.
Zelenskiy has said in the past that Trump would likely change his thinking on Ukraine should he win in November and his call with Trump in July went well, according to three people briefed on the conversation.
But there are signs of growing strain between the two men.
The former president said during a campaign stop earlier in the week that Zelenskiy wanted the Democrats to win the upcoming election. At a separate campaign stop, he said the United States needs to "get out" of the war in Ukraine.
In an interview with the New Yorker published over the weekend, Zelenskiy said Trump's running mate, U.S. Senator JD Vance, was "too radical."
That comment came as Zelenskiy was discussing Vance's plans for ending the war in Ukraine. During a podcast interview earlier in the month, Vance said a potential peace deal in Ukraine would likely involve Russia retaining the land it had already taken, a condition Kyiv considers unacceptable.
