Japan is keen for the troops to leave Okinawa to reduce simmering tensions with local residents, but the United States has said a plan to move the troops to Guam will take decades unless Tokyo picks up much of the approximately $8 billion price tag.
Such spending will be unprecedented and requires parliamentary approval.
The move to Guam is part of the Pentagon's troop realignment plans in the region.
The United States wanted Japan to pay for a quick move outright, but the idea for a loan arrangement emerged in an attempt to gain public support, the Nihon Keizai newspaper reported on Sunday, without citing sources.
Japanese officials are uncertain whether Washington would accept Japan's loan proposal, the Nihon Keizai said.
Defence officials were not available for comment on Sunday.
The two sides in October agreed on a plan that would give Tokyo greater responsibility for security in the Asia-Pacific and are currently trying to finalise the details.
Japan hosts 50,000 US troops, including 14,460 marines, the largest marine contingent based overseas.
Nearly all the marines there are located on Okinawa, where residents have expressed a desire for a rapid reduction in US forces because of long-standing concerns about crimes, safety and environmental problems posed by their presence.
The US military realignment also involves a relocation of a heliport in Okinawa to another base on the southern island, and the assignment a nuclear-powered carrier to Japan for the first time.
American troops have been stationed in Japan since the end of the second world war in 1945.