Former U.S. Army Sgt. Charles Robert Jenkins, who arrived in Tokyo on July 18, is accused of deserting to North Korea in 1965.
Jenkins, 64, married a Japanese woman while living in North Korea where the couple also had two daughters.
U.S. authorities have indicated they want to try Jenkins for defection.
"We will consider requesting custody at an appropriate time. That remains our position," said the U.S. State Department's deputy spokesman, Adam Ereli, when asked about the U.S. position on the issue.
A government spokesman in Tokyo told reporters earlier Wednesday Jenkins, now in hospital, wants to speak to a U.S. military lawyer. But the move did not necessarily mean Jenkins was ready to plead guilty and seek a plea bargain, he added.
Instead of deporting Jenkins for trial in the United States, Japan is seeking a compromise to end the issue.
Jenkins met his wife after she was abducted by North Korean agents in 1978. She returned to Japan with four other abductees in 2002, but had to leave her husband and two daughters behind.