But they also said they have little interest in American individuals or politics and claimed to be indifferent to information from the outside world, according to the report.
The footage taken in Pyongyang and published Monday shows a select group of relatively young North Koreans, both men and women, described by the U.S. network as "ordinary residents."
Not all were willing to speak to CNN, the report stated, but those who did, including a researcher identified as Yu Gwang Chol, said the Trump name is familiar, as well as the name of former U.S. President Barack Obama.
"But we don't really care who is in power in the United States. The point should be whether they would stop a policy of hostility towards my country," Yu said.
North Korea's state-controlled media is the main source of information for most North Koreans, and Pyongyang has defended its nuclear weapons program as a deterrent against a possible U.S. or South Korea attack.
The United States has pledged guarantees of security to Pyongyang over the last several decades, but it is unclear whether the North Koreans CNN interviewed were aware of the history of bilateral negotiations.
Another young North Korean who spoke to CNN said that he, like others, wants a "better relationship" and the end of anti-North Korea policies.
"It could be a good idea on the personal part [for] President Trump to have a meeting with my great leader," said Pak Chol Song, identified as a computer engineer.
In the course of his presidential campaign, Trump had said he would be interested in sharing a hamburger meal with Kim Jong Un, a statement that suggested he would break from protocol in dealing with a country that seeks recognition as a nuclear weapons state.
CNN did not ask North Koreans whether they had heard of the recent assassination of Kim Jong Nam, the older half-brother of Kim Jong Un, at an airport in Malaysia on Feb. 14.
Defector organizations in South Korea say most North Koreans are not even aware Kim Jong Un had an older half-brother.