Trump will visit Seoul on Saturday and Sunday after attending a Group of 20 summit in Japan, prompting speculation that a Trump-Kim meeting could be arranged at the inter-Korean border.
The last time they met was for their second summit in Vietnam in February. Both men walked away without a deal due to gaps over the scope of North Korea's denuclearization and sanctions relief from the US.
A senior US administration official told reporters Monday that there were "no plans" for another meeting. Trump will be in Seoul to see President Moon Jae-in, he said.
A reporter asked Trump at the White House if a summit was mentioned in his latest exchange of letters with Kim.
"Maybe there was, but we, you know, at some point, we'll do that," he replied. "Getting along very well. He's not doing nuclear testing."
The correspondence appeared to have resumed in mid-June after a monthslong lull in negotiations between the sides. Trump revealed on June 11 that he had received a "beautiful" and "very warm" letter from Kim. The North Koreans reported Sunday that Kim had also received a letter "of excellent content" from Trump.
In an interview with The Hill on Monday, Trump was asked to share the details of Kim's letter to him.
"Well, it was a very nice letter. It was actually a 'happy birthday' letter, if you want to know the truth," said the president, who turned 73 on June 14. "It was my birthday. He sent me a beautiful letter -- happy birthday -- which was nice, very nice."
Asked if he sent a letter in response, Trump said, "I sent him a 'thank you' letter. Yeah, I sent him a note."
Neither side has revealed the contents of the missives, but the exchange has raised hopes the two will resume negotiations on dismantling North Korea's nuclear weapons program.
"Appreciating the political judging faculty and extraordinary courage of President Trump, Kim Jong Un said that he would seriously contemplate the interesting content," the North's Korean Central News Agency said Sunday of the letter. (Yonhap)