Rodman, sporting a black t-shirt advertising a cryptocurrency he is involved with, said he was unsure whether he would get to meet with Kim - a man he has previously described as a "friend for life".
North Korean leader Kim Jong-un met with U.S. President Donald Trump on Tuesday in Singapore.
The president then addressed his successes with the rogue nuclear nation to display that the arrangement was a win for the US.
He added that he suspected he "somewhat had something to do with this North Korean situation".
"If diplomacy does not move in the right direction, those measures will increase", he said.
"Meetings between staffs and representatives are going well and quickly. but in the end, that doesn't matter", he said.
He declined, however, to reveal any details of the preliminary discussions being held Monday between USA and North Korean officials.
But when pressed by reporters, the secretary of state would not say whether or not that could include reduction of the number of or removal of US troops in South Korea.
Trump blasts 'haters & losers' in typo-filled tweet from Singapore
President Donald Trump waves from inside his vehicle as he heads into the Istana Presidential Palace, where he will meet with Singapore Prime Minister Lee Hsien Loong, 11 June 2018.
"Thank you for also asking to hold the summit in Singapore", added Mr Lee.
But they were soon smiling and holding each other by the arm, before Trump guided Kim to the library where they held a meeting with only their interpreters.
Sanders, Ambassador Sung Kim, and National Security Council Senior Director for Asia Matt Pottinger will join for the working lunch.
"We have worked very hard to provide access to the media at this event and continually expanded coverage throughout the morning", White House press secretary Sarah Huckabee Sanders told POLITICO in an email. "We appreciate your hospitality and professionalism and your friendship".
Trump continued to tweet angrily at Trudeau from Singapore, saying Monday "Fair Trade is now to be called Fool Trade if it is not Reciprocal". The U.S. president turns 72 on June 14.
Ahead of the meeting, Trump had said he would be able to work out within the first minute whether his North Korean counterpart was serious about making peace.
The spokesman said Trump told Moon he would send Pompeo to Seoul immediately after the summit to explain its outcome.
After being driven separately to the resort island of Sentosa, the two leaders shook hands and exchanged a few words on the steps of the Capella Hotel.
About 2,500 journalists have descended in Singapore to report the summit.
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Plus, for a limited time, customers can pre-order Fire TV Cube and Amazon Cloud Cam together for $199.98 - a $40 savings. The Amazon Fire TV Cube sits at the top end of this scale and we'd pitch the Fire TV Cube at around £120 in the UK.