"If the first one goes okay, we'll have a quick second one," Trump told reporters.
"I would like to do it almost immediately, and we'll have a quick second meeting between President Putin and President Zelenskiy and myself, if they'd like to have me there."
Trump did not provide a timeframe for a second meeting.
He is to meet Putin in Anchorage, Alaska on Friday for talks on how to end the three-and-a-half-year-old conflict in Ukraine.
Trump also said Russia would face consequences if Putin does not agree to stop the war.
"Yes, they will," he said.
He did not spell out the consequences but he has warned of stiff economic sanctions if no breakthrough can be achieved.
Trump spoke after holding talks via telephone with European leaders and Zelenskiy about his meeting with Putin.
"We had a very good call. He was on the call. President Zelenskiy was on the call. I would rate it a 10, very friendly," he said.
Trump has previously said both sides will have to swap land to end fighting that has cost tens of thousands of lives and displaced millions.
On a day of intense diplomacy, Zelenskiy flew into Berlin for German-hosted virtual meetings with European leaders and then with Trump.
Some European governments worry that a land swap could leave Russia with almost a fifth of Ukraine and embolden Putin to expand further west in the future.
Participants in the call with Trump included leaders from France, the United Kingdom, Italy, Poland and Finland as well as European Commission President Ursula von der Leyen and European Council President António Costa.
Zelenskiy said on Wednesday he hoped the Trump-Putin talks will centre on a ceasefire and he warned Trump that Putin was "bluffing" about his desire to end the war.
"I told the US president and all our European colleagues that Putin is bluffing," he said at a joint briefing in Berlin with German Chancellor Friedrich Merz.
"He is trying to apply pressure before the meeting in Alaska along all parts of the Ukrainian front. Russia is trying to show that it can occupy all of Ukraine."
Zelenskiy added that he wanted a three-leader meeting, saying no talks about Ukraine should exclude his country's representatives.
Von der Leyen said that Europe, the United States and the NATO military alliance had strengthened their common ground for Ukraine.
"We have had a very good call," the European Commission president wrote on X after attending a virtual meeting with Trump, European leaders and Zelenskiy.
"Today Europe, the US and NATO have strengthened the common ground for Ukraine," von der Leyen said, adding that "we will remain in close coordination. Nobody wants peace more than us, a just and lasting peace".
with DPA
