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They also didn't rule out a missile test "in the near future" to send a strong message to American forces currently deployed in the region.
The news comes after US President Donald Trump delivered his first State of the Union speech, during which he criticized the Kim Jong Un regime's human rights abuses and "reckless pursuit" of nuclear weapons and ballistic missiles that could soon threaten the US homeland.
Winter Olympics woes
On Monday, North Korea said it canceled a joint cultural performance that was to be held in advance of the Olympics in response to unflattering coverage by South Korean media.
According to a statement from South Korea's Unification Ministry, the North Koreans pulled out because "South Korean media continue to insult North Korea's genuine measures regarding the PyeongChang Olympics and take issues with its domestic festival."
The sources that spoke to CNN said that other planned events could be canceled.
Cracks
Chad O'Carroll, managing director of the Korea Risk Group in Seoul, said the planned military parade could undermine Washington's support of dialogue between the two Koreas.
"The ongoing US support for inter-Korean rapprochement already appears to be showing cracks and will likely be seriously tested in the event of a major DPRK ICBM parade on the eve of the Olympics," he said.
Foreign media will be banned from covering the upcoming military parade, the sources said.
Policy divisions
Cha, a widely respected former academic and former Bush administration official, said in a Washington Post op-ed Monday that the answer to the "real and unprecedented threats" North Korea presents is not, "as some Trump administration officials have suggested, a preventive military strike."
Instead, Cha laid out what he called "a forceful military option available that can address the threat without escalating into a war that would likely kill tens, if not hundreds, of thousands of Americans."