The deadline for the decision is imminent after the US State Department was given 90 days in August to determine whether North Korea should be re-added to the list.
Iran, Sudan and Syria are all currently listed.
Herbert Robert McMaster who advises the White House on terrorism said that Kim Jong-un’s regime appeared to fit the list’s criteria following the murder of the leader’s half-brother earlier this year.
Kim Jong-nam was killed on February 13 at an airport in Malaysia when two women alleged sprayed him with the nerve agent VX.
Mr McMaster said: “A regime who murders someone in a public airport using nerve agent, and a despotic leader who murders his brother in that manner, I mean, that’s clearly an act of terrorism that fits in with a range of other actions.”
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US and South Korean officials have claimed the assassins were acting on the orders of Kim Jong-un but North Korea has denied any involvement in the murder.
Kim Jong-un’s rogue nation was first added to the list in 1988 after an airline bombing that killed more than 100 people.
In 2002 the then US President, George W Bush, described North Korea as being part of an “axis of evil” along with Iraq and Iran but it was removed from the list by Barack Obama in 2008 following progress in denuclearisation talks.
However, over the last few months Pyongyang has carried out a number of nuclear missile tests and threatened to launch an attack on the American territory of Guam.
Admitting that the US is considering re-listing North Korea as a state sponsor of terrorism Mr McMaster said: “The President’s Cabinet is looking at this as part of the overall strategy on North Korea.”
Countries on the list face a range of sanctions including restrictions on defence sales and a ban on foreign assistance.
The Trump administration decided to leave North Korea off its latest list of state sponsors of terrorism which was published in July.
But Donald Trump has taken a hardline on the threat of North Korea and has emphasised that he will “do what has to be done” to remove the threat of North Korea.
Addressing the United Nations in September Mr Trump drew criticism when he mocked the state’s leader by referring to him as “rocket man on a suicide mission.”
He also said that “military action would certainly be an option” for dealing with Kim Jong-un.