Mr Trump told reporters in Washington DC that "a good dialogue" was taking place with North Korea, but sanctions on Pyongyang would remain in place.
Mr Trump met North Korean leader Kim Jong-un last June, the first such meeting for a sitting US president.
No tangible progress has been achieved so far on the main US goal: North Korea's denuclearisation.
President Trump said last week that he had received a "great letter" from Mr Kim, although he did not reveal its contents.
"We are negotiating a location," he told reporters at the White House on Sunday.
"It will be announced probably in the not too distant future. They do want to meet and we want to meet and we'll see what happens."
He said the US had "a very good dialogue" with North Korea, adding that he had "indirectly spoken" with Mr Kim.
Mr Trump said US sanctions would remain "in full force and effect" until the US saw "very positive" results.
At the June summit in Singapore, the two leaders signed an agreement to work towards the denuclearisation of the peninsula. But it did not include a timeline, details or any mechanisms to verify the process.
In a closely watched New Year's Day address, Mr Kim said he was still committed to denuclearisation but warned that if the US did not lift sanctions he would consider taking a different path.
The North reacted angrily last month when the US slapped fresh sanctions on three senior officials, after a report revealed a raft of human rights abuses.
Pyongyang expressed "shock and indignation" at the new US measures, saying that the US policy of "maximum pressure" would be its "greatest miscalculation".
North Korea is also subject to various sets of United Nations Security Council sanctions related to its banned nuclear and ballistic missile weapons programmes.