Spokesmen from the prime minister's office, Foreign Ministry and Defense Ministry could not confirm the reports.
The dispute over Futenma has strained ties between the two allies and trading partners, and the U.S. had hoped for a decision by year-end.
According to a 2006 agreement between Japan and the U.S. to reorganize American troops in Japan, Futenma was to be moved to a less crowded part of northern Okinawa, but Hatoyama has said the relocation site could be changed - perhaps even off the island.
Okinawa residents complain about base-related noise, pollution and crime, and many want the airfield closed and its functions moved off the island entirely.
The 2006 reorganization plan, made under the previous conservative Tokyo government, was aimed at lightening the load on Okinawa, which hosts more than half the 47,000 U.S. troops in Japan under a security pact.
Part of the plan involved moving about 8,000 Marines from Okinawa to the U.S. territory of Guam by 2014, but the U.S. military says that plan cannot move forward until Futenma's replacement facility is finalized.
Hatoyama, whose party came to power in a landslide election in August, has promised that Tokyo would adopt a less subservient relationship with Washington, but has also stressed that the U.S. security alliance was the cornerstone of Japan's diplomacy.
His Cabinet is divided and has sent mixed signals on what to do about the future of Futenma. The leader of a left-leaning junior coalition partner has hinted her party would withdraw from the government if the base is moved to Nago.
Foreign Minister Katsuya Okada and Defense Minister Toshimi Kitazawa have said it would be difficult to find a site not on the island, and have suggested honoring the current agreement. Kitazawa visited Guam recently to check out other options, but warned that pushing for a major change in the plan would hurt trust between the two allies.