Democracy and Class Struggle says the meeting in Beijing is to repair the bridge before crossing the water.
Improved Chinese North Korean relations are important before the summit with South Korea.
South Korea's left-leaning press Hankyoreh also reported Kim had travelled to Beijing for meetings with Chinese President Xi Jinping on Monday afternoon before leaving for a "third location" on Tuesday.
It did not cite specific sources.
The Hankyoreh did not specify where the "third location" was but said it could be in China.
Hong Kong's South China Morning Post said Kim was on the train that left Beijing, citing two anonymous sources.