"New relocation options will be considered, but by setting a deadline for May next year, [the government] hopes to win the understanding of the United States," the mass circulation newspaper said.
A similar report on Japan's Kyodo newsagency said the decision had been put off until next year.
The plan under a 2006 deal agreed between the US and Japan is to relocate Futenma to a less crowded part of northern Okinawa, but Hatoyama has said the new site could be changed, perhaps even off the island.
|Okinawa residents are unhappy about noise, pollution and crime from the base [AFP]
Okinawa is home to more than half the 47,000 US troops in Japan under a security pact, but their presence is regular source of friction with local residents that has led to mass protests.
Residents have regularly complained about base-related noise, pollution and crime, and many want the airfield closed and its functions moved off the island entirely.
The 2006 plan also involves moving some 8,000 marines from Okinawa to the US territory of Guam by 2014, but the US military says that plan cannot move forward until Futenma's replacement facility is finalised.
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 US security alliance was the cornerstone of Japan's diplomacy.
The plan to move Futenma is part of a broader realignment of US troops in Japan against a background of China's rising power in the region and an unpredictable North Korea.