Trump said Putin wanted to make a deal to end the nearly four-year-old war, adding he thought Zelenskiy was also ready to reach an agreement.
Both leaders backed away from an agreement before, but a deal was now "reasonably close", Trump said in a discussion after his prepared remarks to world leaders and business executives in Davos, Switzerland on Wednesday.
Trump twice said he would meet with Zelenskiy later on Wednesday, a fact disputed by a source familiar with Zelenskiy's schedule, but later said the meeting was planned for Thursday.
Ukraine will mark the fourth anniversary of Russia's full-scale invasion on February 24.
Trump said he had expected to negotiate a deal to end the war sooner, but there was "abnormal hatred" between the two leaders.
Last week, Trump told Reuters that Zelenskiy was the main impediment to reaching an agreement.
Washington was getting closer to brokering a ceasefire agreement, he said on Wednesday.
"I think I can say that we're reasonably close," he said.
"We have to get it stopped ... I believe they're at a point now where they can come together and get a deal done. And if they don't, they're stupid."
Trump told reporters that Putin had accepted his invitation to join his Board of Peace initiative aimed at resolving global conflicts, but the Russian leader said Moscow was still studying the proposal and would respond in due course.
Putin, quoted by Russian news agencies at a meeting of Russia's Security Council, said he believed the proposed board was mainly designed to deal with a Middle East peace settlement.
He said Russia was prepared to provide $US1 billion ($A1.5 billion) for the board - as proposed by Trump for long-term membership - from frozen Russian assets.
However, that plan was likely to meet resistance from Ukraine, which says it needs those assets to rebuild the country.
