A spokesperson for the defence ministry declined to comment on the reports on Thursday.
The US Air Force, which was operating the hybrid aircraft carrying eight people, has called Wednesday's incident off Yakushima island a "mishap" and said the cause is currently unknown.
The crash happened about 2.47pm (local time) near the island's airport.
Witnesses said the plane's left engine appeared to be on fire as it approached the airport for an emergency landing in clear weather and light winds, media reported.
Developed by Boeing and Bell Helicopter, the V-22 Osprey can fly like both a helicopter and fixed-wing aircraft and is operated by the US Air Force, Marines and Navy, and the Japan Self-Defence Forces.
The deployment of the hybrid aircraft in Japan has been controversial, with critics saying it is prone to accidents.
The US military and Japan say it is safe.
In August, a US Osprey crashed off the coast of northern Australia while transporting troops during a routine military exercise, killing three Marines.
Another crash-landed in the ocean off Japan's southern island of Okinawa in December 2016, prompting a temporary US military grounding of the aircraft.