Trump told reporters travelling home to Washington with him aboard Air Force One from Argentina that "three sites" were in consideration for the meeting, a follow-up to their historic summit in Singapore in June.
When asked about a future meeting, Trump said: "I think we're going to do one fairly (soon) -- into January, February, I think."
Trump had been in Buenos Aires for the Group of 20 summit.
In June, Trump and Kim opened up dialogue on denuclearisation of the Korean peninsula after months of trading military threats and pointed barbs.
The two leaders signed a vaguely worded document on denuclearisation of the peninsula, but progress since has stalled as Washington and Pyongyang spar and North Korea has taken few concrete steps to abandon its nuclear and ballistic missile programs.
They agreed on the need for "maintaining vigorous enforcement of existing sanctions to ensure the DPRK understands that denuclearisation is the only path," Sanders said, using the North's official name, the Democratic People's Republic of Korea.
But differences have emerged between Washington and Seoul on how to proceed with Kim, as the dovish Moon has long favoured engagement with the North.
When asked Saturday if he would ever host Kim in the United States, Trump replied: "At some point, yeah.
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