According to the Dong-a Ilbo
newspaper in Seoul, the North could fire the missile as early as mid-June - around the time Lee Myung-bak, the South Korean president and Barack Obama, his American counterpart, are to meet in Washington.
South Korea's Yonhap news agency also reported that the long-range missile may be a modified version of a Taepodong-2, which the North tested in 2006, and in April.
Meanwhile, Lee Myung-Bak warned on Monday that his country would "never tolerate" the North taking a "path of military threats and provocation".
However, North Korea says it will bolster its nuclear programme.
The North "will further strengthen its nuclear deterrent in order to safeguard its ideology and system," the official Korean Central News Agency (KCNA) said in a commentary on Monday.
North Korea has another site at Musudan-ri on the east coast, where it launched a rocket in early April.
Pyongyang said it put a satellite into orbit but other nations saw the rocket launch as a disguised missile test.
Tensions on the Korean peninsula remain high after North Korea conducted a nuclear test for the second time, and launched a series of short-range missiles.
|The North Korean leadership continues to defy international criticism of its actions [AFP]
Responding to international and regional criticism of the tests, Pyongyang then declared the armistice which ended the war with South Korea in 1953 to be over and threatened "self-defence measures" if the UN imposes new sanctions.
The United States and South Korea then raised the alert level for their security forces a day after North Korea said it was scrapping the armistice.
The South Korean defence ministry said on Thursday that the US-South Korea Combined Forces Command had raised its alert level from stage three to two.
The alert level is the highest since North Korea's first-ever nuclear test in 2006.