Rebecca Coriam's parents believe she was raped and thrown overboard in 2011, and have hired a private investigator.
Now case notes written by a police chief in the Bahamas reveals claims that the 24-year-old was caught up in a love triangle before she went missing.
She was reported as missing from the Disney Wonder vessel in March 2011 as it sailed near Puerto Vallarta, Mexico.
Disney claim the Liverpool student was swept overboard by a freak wave.
Notes made by Superintendent Paul Rolle, seen by the Liverpool Echo, suggested Rebecca had been involved in a threesome before her death.
The notes state: '(American woman in relationship with Rebecca) left to get more beer.
'Came back and Rebecca and (male crew member who was in a relationship with the American woman) chatting.
'She came back and all 3 went to (male crew member’s) room. (Male crew member) had sex with both. (American woman) left the room again to get beer. Came back and Rebecca and (male crew member) had sex.'
The investigator also said the male had a 'very nonchalant attitude' and was 'laughing and joking' - to the point he was given a warning.
Names of the potential suspects, one man and one woman, are known to private investigators.
Two of the Liverpool student's best friends visited the Coriam parents after she went missing, and said their friend had voiced fears of being raped or sexually attacked while on the ship.
Maritime expert Bill Anderson said: 'What her best friends said to the Coriams sent a shiver down their spines.