The report also said that North Korean investigators were checking the journalists' cameras, video tapes and notebooks to try to establish if they had been spying on the North's military facilities.
An unnamed South Korean intelligence officer was quoted as telling the paper the two would undergo interrogation but were not likely to be treated harshly.
The report said the women walked across the frozen Tumen river marking the northeastern border between China and North Korea while filming a programme on North Korean refugees.
Earlier reports have suggested the two may have been seized after North Korean border guards crossed into Chinese territory.
The journalists work for Current TV, a California-based online media outlet founded by Al Gore, the former US vice-president.
The incident comes amid heightened tensions on the Korean peninsula.
Ties between Washington and Pyongyang are already strained over the North's refusal to fully verify its past nuclear activities as well as its plan to launch a satellite into orbit in April.
North Korea and the US do not have diplomatic relations and lines of communication between the two countries are limited.
The National Intelligence Service, South Korea's main spy agency, said on Tuesday that South Korean and US intelligence authorities had been keeping a close watch on the case, but that it could not immediately confirm the Joong Ang Ilbo report.
A US official said on Saturday that Washington has been in touch with North Korean representatives about the journalists and was awaiting a reply.