The US president made the suggestion the day after North Korea threatened to pull out of the summit planned between the two leaders for 12 June in Singapore.
Mr Trump added that if the North Korean leader agrees to denuclearisation, he will get “protections”.
“He’ll get protections that would be very strong,” the US president said on Thursday.
And for the second day in a row, he said the US has not been told anything about the summit.
He remained nonchalant about the issue, saying if the meeting with Mr Kim happens, “it happens, and if not we go on to the next thing”.
But he did add that the “best thing” the North Korean leader could “ever do” is make a deal.
White House spokeswoman Sarah Huckerbee Sanders added: “Nothing has changed on our end.
“This was an invitation that North Korea offered, and that we’ve accepted, and we’re continuing to move forward in those preparations.”
Mr Trump also said the two countries have been planning details and “are continuing to negotiate in terms of location, the location as to where to meet, how to meet, rooms, everything else”.
“They’ve been negotiating like nothing happened,” he added.
Despite the North threatening to pull out over the annual military drills the US and South Korea started on Friday, the US remained defiant.
Pentagon spokeswoman Dana White said there are no plans to change or reduce the scope of the joint Max Thunder drills between the two countries’ air forces.
She said the exercises are long-planned, are defensive in nature and are meant to ensure the readiness of US and South Korean forces.
Exercise Max Thunder finishes on 25 May and includes aircraft from across the US military services.
On Wednesday North Korea cancelled a second round of talks with South Korea with hours to go in retaliation over the drills.
Mr Trump attempted to allay their fears on Thursday by saying the US is not thinking of a “Libya model” for the denuclearisation of the North.
North Korea’s first vice foreign minister Kim Kye Gwan on Wednesday warned the fate of the US summit and relations between the two countries “would be clear” if Washington spoke of a Libya-style denuclearisation for the North.
Mr Kim appeared to be responding to recent comments made by Mr Trump’s security adviser John Bolton and others suggesting North Korea should follow the “Libyan model” of nuclear disarmament.
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Libya cut its nuclear programme in exchange for the easing of sanctions.
North Korea, however, sees the gruesome death of Libya’s leader Muammar Gaddafi in 2011 as justification for its own nuclear development amid what it describes as US threats.