Sir Keir Starmer suggests Andrew Mountbatten-Windsor should testify over his dealings with the convicted sex offender.
The woman, then in her 20s, says the alleged encounter happened at Royal Lodge in 2010.
In some of the cases Scotland's prosecution service is considering whether to bring corporate homicide charges.
Sir Keir and Sanae Takaichi discussed ways to strengthen ties between their two nations during the meeting, at the end of the UK prime minister's trip to East Asia.
The councillor was chosen after Greater Manchester mayor Andy Burnham was blocked from standing.