The alleged rape occurred after the crew went out for the night, according to The Sun.
The Singapore Police Force confirmed on Thursday that a report had been filed and that investigations are ongoing, Channel News Asia reported.
The accused man is said to have worked for British Airways for several years.
British Airways has sent representatives to Singapore to cooperate with local authorities in connection with the case.
No further details about the alleged perpetrator have been released.
Under Singapore law, rape and sexual assault by penetration are punishable by up to 20 years in prison, along with a possible fine or caning.