The preparations include the installation of measuring equipment near the entrance to an underground test site in Pungye-ri in North Korea's northeast Hamgyong province, the report said.
Separately, Yonhap News said the installation of the radiation measurement equipment may indicate a test is imminent.
The Pungye-ri test site is where the Communist country conducted its two previous nuclear tests in 2006 and 2009, Japan's Kyodo News reported.
There have been increasing threats from North Korea about going ahead with its third nuclear tests ever since the U.N. Security Council approved a resolution last week tightening its existing sanctions imposed after the North's earlier nuclear and missile tests. The latest resolution came after the North, in defiance of those sanctions, went ahead last month with a long-range rocket launch, claiming it was to place a satellite in space. Critics, however, saw it as a cover by the North to test its inter-continental ballistic missile capability.
The Chosun Ilbo also said South Korea and the United States are considering military steps, besides economic sanctions, if the North goes ahead with its third nuclear test.
South Korea already has warned the North would face grave consequences if it conducts the test.
The Chosun Ilbo report quoted a government official as saying: "We believe North Korea could conduct a nuclear test as early as tomorrow if it wants to, so we are closely monitoring the situation."
Meanwhile, South Korea's President-elect Park Geun-hye planned to meet Friday with a visiting U.S. Congressional delegation led by Ed Royce, R-Calif., the chairman of the House Foreign Affairs Committee, to discuss the North Korean situation, Yonhap News reported.