Ms Finley, a drug addict, was associated with the city's prostitutes and may also have worked as one. She had been living in the Huskisson Street area, a red light district just outside Liverpool city centre.
Detective Chief Inspector Francis Youell said yesterday: 'There are always people about who frighten these girls for various reasons, and the girls learn to be streetwise and aware of these people and won't get in a car with them.
'These are the people I want to hear about. My officers are in the area now, but I am not interested in what the girls are doing there - that's not my problem. It is a question of trust.
'They have got to be prepared to accept that the police are not in the business of stopping them performing their work - we are out to protect them from any similar attacks.'
Meanwhile, a detective from Merseyside went to Leicester yesterday to attend a meeting of officers investigating links between the murders of five women in the Midlands and South Yorkshire in the past eight months.
A connection with Ms Finley's murder has not been ruled out, although police said that there was nothing to connect the case as yet.