North Korea has carried out illicit trading through small Chinese banks. The sanctions proposed would have to threaten to prohibit those banks from the international finance system and make it undesirable for them to do business with the North.
In addition, the U.S. may try to seize additional assets from Kim and his family outside North Korea.
Mr. Trump is scheduled to meet with Chinese President Xi Jinping next month, and North Korea is expected to be high on the agenda.
The President met with H.P. McMaster, his national security adviser on Saturday to discuss the situation about North Korea. He came to the conclusion that the North is "acting very, very badly," after the country's rocket-engine test believed to be part of their missile program to have the capability of reaching the U.S.