"The launch is coming closer. The possibility is high that the launch date will be set for April 12 or 13," the source said, according to the Tokyo Shimbun in a report from Seoul.
It cited the source as saying that North Korea had begun injecting liquid fuel into the rocket.
The paper also said a diplomatic source had confirmed that North Korea has moved the rocket to a launch pad in Tongchang-ri in the country's far northwest.
Japan's newspapers pay close attention to North Korea and often lead the international media in breaking stories on the hermit state, sometimes ahead of their South Korean counterparts.
The Tokyo Shimbun in particular is known for its connections with Kim Jong-Nam, the older brother of Pyongyang's new leader, Kim Jong-Un.
South Korea's defence ministry in Seoul had no immediate comment on Thursday's report, but was scheduled to hold a press briefing later in the day.
The military in Seoul said it had no information on whether the rocket was being fuelled.
The report came after North Korea insisted on Tuesday it would go ahead with what it insists is a satellite launch, snubbing a call from US President Barack Obama to drop the plan and accusing him of a "confrontational mindset".
The US has suspended plans to send food aid to North Korea, saying it has broken a promise to halt missile launches and cannot be trusted to give help to those who need it, a Pentagon official said on Wednesday.
Under a deal reached in February, North Korea had agreed to a partial nuclear freeze and a missile test moratorium in return for US food aid.
The West and North Korea's Asian neighbours have urged Pyongyang to scrap the rocket launch, which is seen as a pretext for testing ballistic missile technology that is banned under UN resolutions.
The preparations for the rocket launch "have entered a full-fledged stage of action", Pyongyang's foreign ministry spokesperson said last Friday in a statement, according to North Korea's state media KCNA.
"The projected launch of the working satellite is a gift to be presented by the Korean people to the centenary of the birth of President Kim Il Sung," the grandfather of the hermit nation's young leader Kim Jong-Un and the nation's founder, it said.
The nuclear-armed state insists it has a right to launch a satellite for peaceful purposes.
The North says the satellite will estimate crop yields and collect weather data after a long-range rocket puts it into orbit in April.
The home-built satellite will also assess the country's forest coverage and natural resources, the official news agency said late on Wednesday in another attempt to stress the purportedly peaceful nature of the exercise.
The satellite weighs 100kg and will follow a "solar synchronous orbit" at a height of 500km, with a lifespan of two years, it quoted an unidentified senior official from the Korean Committee for Space Technology as saying.
The North has said it has invited experienced space experts and foreign media "to observe the course of the launch in order to prove the peaceful nature of a scientific and technological satellite launch in a transparent manner".
Japan, regularly the target of North Korean barbs, said this week it will deploy surface-to-air missiles in central Tokyo in addition to facilities on the southern island chain of Okinawa, in readiness for the launch.