US and South Korean troops are currently on high alert after the North said it was no longer bound by the truce that ended the Korean war in 1953.
The hardline North, under President Kim Jong-il, has threatened military action against the South after Seoul’s decision to join a US-led security initiative under which North Korean ships could be stopped and searched.
Hosting a summit of South-East Asian leaders in Seogwipo, South Korea, President Lee Myung-bak warned the North against further provocative acts.
Monday’s newspaper reports said North Korea’s construction of the new launch site at Dongchang-ni was now near to completion.
Previous long-range missiles have been fired from a site on the country’s north-east coast.
The missile is believed to be a version of the Taepodong-2 rocket which was fired on 5 April.
It has a range of up to 6,500km (4,000 miles), the JoongAng Ilbo reported, which would put Alaska within striking range.
According to South Korea’s Yonhap news agency, the missile has been moved to the Dongchang-ni launch base, about 65km (40 miles) from the Chinese border.
The Chosun Ilbo added that North Korea had also designated a large area off its west coast a “no-sail” zone until the end of July.
US Defense Secretary Robert Gates said there were signs of work being done on a long-range missile, but he said the North’s intentions were not yet clear.