The scheme would be similar to 'Sarah's Law' - the law introduced in England, Scotland and Wales in 2011..
It allows a parent or guardian to ask police if a person who has contact with children is a child sex offender.
Hundreds of paedophiles have been identified in Great Britain since the introduction of the scheme.
Two DUP assembly members, Paul Frew and Lord Morrow, have tabled an amendment to the Justice Bill due to be discussed in the assembly on Tuesday.
The amendment says that guidance for statutory agencies managing the risks of offenders must "contain arrangements for the consideration of disclosure, to any particular member of the public, of information in the possession of the agencies about the relevant previous convictions of any specified sexual or violent offender, where it is necessary to protect a particular child or children from serious harm caused by the offender."
The amendment also states that members of the public provided with information may be prevented from disclosing it to any other person.
Sarah's Law was named after eight-year-old Sarah Payne, who was murdered by paedophile Roy Whiting in July 2000.
The DUP is proposing the introduction of a paedophile disclosure scheme in Northern Ireland.