Trump has already called on
China to take action to rein in North Korea, over which China has considerable influence and leverage, the official said.
"You gotta work on North Korea," Trump told a Chinese official on February 27, the senior administration official said, apparently pointing to a brief meeting at the White House between Trump and Chinese State Councilor Yang Jiechi, the highest-ranking Chinese official Trump has met with since taking office.
North Korea has successfully developed nuclear weapons, but still lacks a delivery method, the official said. Still, the US administration is concerned that North Korea could purchase a delivery method.
Trump is not the first US president to be alarmed over North Korea's nuclear program.
The senior official who spoke to reporters February 28 on the condition of anonymity said President Barack Obama on his final day in office told Trump he believed North Korea is the biggest national security threat to the US.
Trump previously referred to the conversation during an interview last month with Fox News, but declined to reveal what Obama relayed, other than to call it "a military problem with a certain place."
Trump's concern over North Korea
is in part fueled by his belief that North Korea's leader Kim Jong Un "may be crazy," the official said.
The question for Trump, though, has been, "Is he crazy or is he smart and strategic?" the official said, relaying Trump's thinking.
The senior administration official also pointed to North Korea's alleged role in orchestrating the assassination of Kim's half-brother as a sign of the country's capabilities.
Trump has publicly expressed concern about North Korea's nuclear program and has said that he believes the US should leverage China's cooperation in helping to dismantle North Korea's nuclear program, claiming on the campaign trail that China has "total control over North Korea."
"China should solve that problem," Trump said last year. "And if they don't solve the problem, we should make trade very difficult for China."
Still, the senior administration official said Trump believes the US has a good relationship with China and expressed optimism about the prospects of enlisting China's help in controlling Pyongyang.