The Japanese newspaper reported "the launch is coming closer" and said the launch date "will be set for April 12 or 13."
"Tokyo Shimbun" cited a source close to the government in North Korea as saying liquid fuel is being injected into the rocket.
Pyongyang has said it will go ahead with the launch, which it says is aimed at putting a satellite into orbit.
Western and neighboring Asian countries see it as a North Korean attempt to develop a long-range missile capable of carrying nuclear warheads.
North Korea reportedly will permit foreign observers to attend the launch, in an apparent move to defuse international criticism.
The report on the observers, from South Korea's Yonhap news agency, came after the United States said it was suspending a plan to send badly needed food aid to the North in response to the planned rocket launch.