The secretive state has topped the Open Doors World Watch List as the country where Christians face the most persecution since 2002.
But of the three, only Kim Dong Chul was arrested before Trump became president in January 2017.
A USA official said on Wednesday the US government was looking into the reports.
The venue makes the most sense logistically for Kim, the source said, because media facilities and equipment are already in place, which could allow the summit to take place "in late May".
Analysts say Kim would have asked China, North Korea's only major ally and main economic lifeline, to soften its enforcement of sanctions aimed at the North. Kim also may have sought Chinese commitments to strongly oppose any military measure the United States might take should his talks with Trump fall apart and the North starts testing missiles again.
An official with South Korea's Blue House disputed The Times' report, saying that a US National Security Council representative assured them that the report was "not true", according to Yonhap News.
The only explanation for their arrest came from North Korea's state news agency, KCNA, which described their offenses as "hostile criminal acts with an aim to subvert the country".
US Vice President Mike Pence is postponing his plans to travel to Brazil this month in order to ensure foreign policy resources are focused on Trump's talks with Kim, Pence's spokeswoman said.
Past year the North staged its most powerful nuclear test to date and launched missiles capable of reaching the USA mainland as Kim and Trump traded threats of war and personal insults, sparking global security fears.
Kim had made the comments during his summit with South Korean President Moon Jae-in on Friday at a border truce village. "I don't know", she said.
"China is willing to strengthen communication with North Korea and continue to play a positive role in seeking a political solution to the Korean peninsula issue", he said.
"The only thing we can do is rub their noses in this". The families of the prisoners, meanwhile, said they had received no new information about their loved ones. "You can't negotiate. You just have to shame them".