The proposal is based on Helen’s Law, which was passed by MPs at Westminster in March.
It will also apply to those convicted of manslaughter and child sex offenders who do not reveal a victim’s identity.
The motion has been supported by the families of Lisa Dorrian and Charlotte Murray whose bodies have not been found.
Lisa Dorrian, from Bangor, was last seen at a caravan site in Ballyhalbert in Co Down in 2005.
Detectives believe she was murdered by someone she knew, but no-one has been convicted.
Her sister Joanne, speaking on the 15th anniversary of her disappearance in February, said her family’s lives have been “ruined” by what happened.
Charlotte Murray, from Omagh, disappeared in 2012.
Her ex-fiance Johnny Miller was found guilty of her murder in 2019 and is serving a 16 year life sentence tariff without parole.
Speaking in February 2020, after Miller was told he must serve a minimum 16 years of his life sentence, Charlotte Murray’s sister Denise said the family wanted to say its goodbyes “in peace”.
The Prisoners (Disclosure of Information About Victims) Bill, known as Helen’s Law, followed the murder of Helen McCourt in Merseyside in 1988.
Her killer Ian Simms was released from prison without disclosing the location of her remains.
Monday’s motion, put forward by the DUP, calls for the Justice Minister Naomi Long to “introduce urgently equivalent legislation” and “recognises the ongoing pain and trauma experienced by families in Northern Ireland”.
It would place “a statutory obligation on the Parole Board to take into account an offender’s non-disclosure of such information when making a decision about their release from prison”.
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