The news follows the pair's historic meeting in Singapore earlier this morning.
Trump said the agreement signed at the Singapore summit was the first step in a long journey to improve relations with North Korea.
The US President has vowed to "end war games" in a "new chapter" with North Korea.
He said it is important Kim visits the US to continue this but admitted this will be at "the appropriate time".
Kim Jong-un has never visited the US.
But Trump has now invited Kim to the White House, with an official invite believed to be being drafted.
In recent years, he may have been at serious risk in the US due to the strained relations between the two countries.
The tubby tyrant, who was educated in Switzerland, often leaves North Korea for important trips.
The US President reportedly wants to further discuss human rights with Kim.
It might mean Trump will visit North Korea for the first time.
The grandfather said he is open to a visit to the nation's capital Pyongyang "some day".
The pair shook hands earlier, then held a 41 minute private meeting.
But the US President dropped a real clanger when he appeared to make a fat joke during his high-profile summit with chubby Kim Jong-un.
And he showed off to the North Korean dictator by giving him a peak inside his magnificent £1.5million limo “The Beast”.
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