The president tells reporters that there are three sites under consideration, but he's not identifying them.
Trump and Xi agreed that "great progress has been made with respect to North Korea", the White House statement added.
"And the message was that President Trump has a very friendly view of Chairman Kim and that he likes him, and so he wishes Chairman Kim would implement the rest of their agreement and that he would make what Chairman Kim wants come true", he said.
Last month, a planned meeting between U.S. Secretary of State Michael Pompeo and North Korean official Kim Yong Chol to discuss details of a potential second summit was called off.
Trump had been in Buenos Aires for the Group of 20 summit.
North Korea has taken few concrete steps to abandon its nuclear and ballistic missile programmes.
'At some point, ' he will, Trump said about hosting Kim in the United States, with this weekend's announcement raising the spectre of such a trip being just weeks off.
The pair "reaffirmed their commitment to achieve the final, fully verified denuclearisation" of North Korea, Mr. Trump's spokeswoman Sarah Sanders said.
Central Intelligence Agency chief Haspel to brief Senate on Khashoggi killing
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South Korean President Moon Jae-in, second from right, is greeted by North Koreans as North Korean leader Kim Jong Un, right, watches during a welcome ceremony at Sunan International Airport in Pyongyang, North Korea, Sept. 18, 2018.
On Friday, a South Korean train left for North Korea, launching an 18-day inspection of railways there as part of efforts to eventually connect rail lines over the border, a project their leaders agreed on earlier.
The South Koreans have expressed hope the visit - which would be a first for a North Korean leader - could happen by the end of this year.
They have also begun work to reconnect a train line and fix another rail link across the border.
Moon said Kim visiting Seoul by the year's end may still be possible, but it would be up to Kim to decide.
Moon's approval rating has declined for nine straight weeks since hitting 65.3 percent in late September following his third summit with North Korean leader Kim Jong-un in Pyongyang.