One concerned man claimed a known paedophile had been seen using a property off Spencer Road, and said he should not be allowed to live so close to a school, church grounds and a play park.
"If these people are sick and if they are going to be rehabilitated then they should be rehabilitated away from places where children are known to gather. I do know that a paedophile has been seen there."
A landlord confirmed that a known and convicted sex offender had approached him earlier this year about renting a property for himself and a new girlfriend.
"He had registered with an estate agent in the area and had been referred to him. He told me that his girlfriend was currently living in a hostel because she had been diagnosed with depression, but that he had taken her our for the day to his current house and he felt she would be much better of living with him than in care."
Meanwhile, Alderman William Hay, said any housing of sex offenders so close to a school "worried him".
"Something like this would worry the wider community and especially parents. Some may say these people have to live somewhere, but I really do feel that they should not be located near schools or churches and especially not where young people might be out and about. I think consulting with the wider community would have been important, and I don't believe that has happened.
Mr Hay went on to warn against any form of vigilante behaviour against sex offenders, saying: "Two wrongs do not make a right."
Claims that a property was operating as a paedophile rehabilitation unit were flatly denied by those operating MASRAM (Multi-Agency Sex Offender Risk Assessment and Risk Management) - the process which exist(s) for the assessment and management of risk posed by sex offenders.
A spokesperson said: "There are only six Probation-approved premises (hostels) in Northern Ireland. Five of these can at times house sex offenders - none of the six are in the Waterside nor indeed are any of them in the County of Londonderry.
"Where members of the public have concerns about any individual the appropriate course of action is to report those concerns to the police," he said.