Trump made the remark while he met with Moon Jae-in, South Korea's president, for pivotal discussions ahead of the American president's planned meeting with the North Korean dictator.
"Whether or not it happens, you'll be knowing pretty soon," Trump told reporters at the White House. He also declined to say whether he has spoken with North Korea's leader.
The summit is scheduled for June 12 in Singapore, which is widely viewed as a neutral site. Yet doubts continue to grow about whether the meeting will actually take place. Trump's remarks Tuesday were the strongest indication yet that the summit might not happen as planned.
Last week, North Korea said it would reconsider whether to hold the meeting after abruptly canceling talks with South Korea amid joint military drills with the U.S. on the Korean Peninsula.
The communist dictatorship also took issue with Trump's national security advisor, John Bolton, who suggested using a denuclearization model similar to one used with North African country Libya. The nation's dictator at the time, Moammar Gadhafi, agreed to give up nuclear weapons in exchange for relaxed U.S. sanctions. Eventually, however, the U.S. supported a violent overthrow of Gadhafi.
North Korea called any attempt to impose a Libya-style arrangement on the country "awfully sinister." Trump has said, though, that the "Libyan model isn't a model that we have at all."
"There was a somewhat different attitude after that meeting," the U.S. president said of Kim. "I can't say that I'm happy about it."
The South Korean president on Tuesday struck a more optimistic note about the planned summit between Trump and Kim. Moon pushed back against U.S. skepticism about the meeting and said he is confident that Trump will make the summit a success.
In his remarks Tuesday, Trump did say that he believes Kim is "absolutely very serious" about denuclearization. The Trump administration has made it clear that it wants North Korea to give up its nuclear weapons program.
Trump also made some promises to the North Korean leader Tuesday.
"He will be safe, he will be happy, his country will be rich," Trump said. "Kim will be extremely happy if it works out."
The president added the meeting won't happen if certain conditions aren't met. He also said a summit could happen further down the road if it doesn't occur next month as planned.
No sitting U.S. president has met face-to-face with a North Korean leader.