Kim Sang-duk (also known as Tony Kim) was detained on espionage charges in 2017 and two weeks later, Kim Hak-song was held on suspicion of "hostile acts".
Kim Dong-chul, a pastor in his early 60s, was detained in 2015 on spying charges and sentenced to 10 years' hard labour in 2016.
Mr Trump tweeted that we should "stay tuned" for news.
As everybody is aware, the past Administration has long been asking for three hostages to be released from a North Korean Labor camp, but to no avail. Stay tuned!
— Donald J. Trump (@realDonaldTrump) May 3, 2018
The secretive state has topped the Open Doors World Watch List as the country where Christians face the most persecution since 2002.
Explaining the reason behind this, Beth Fuller from the charity Open Doors told Premier: "For Christians, because they dare to say there's a higher authority than Kim Jong-un and his ruling elite, they are just immediately arrested, imprisoned and quite frequently killed if their faith is discovered."
The US State Department has said it can not confirm the validity of the reports on the prisoner move.
Fuller told Premier there are many people in the secretive state that have been imprisoned for their faith.
"Sadly, they [Sang-duk, Hak-song and Dong-chul] are just a few examples of the tens of thousands of people that are imprisoned in North Korea in just horrific labour camps - on the sort of level of the concentration camps of the Second World War."
She urged Christians to continue praying for the "protection over Christians in that country, especially those who are following Jesus in secret... that they would really be able to keep their faith hidden".
Listen to Beth Fuller speaking with Premier's Eno Adeogun:
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