Scottish-born Black was convicted of murdering Morley schoolgirl Sarah Harper and three other children, but suspected of many more.
He died of heart disease in a Northern Ireland prison in 2016 at the age of 68.
The paedophile from Falkirk was a delivery driver who stalked the roads of the UK searching for victims.
Sarah, of Brunswick Place, was on her way back from a nearby corner shop when she was snatched and murdered in 1986.
Four weeks later, a dog walker found the 10-year-old's body floating in the River Trent at Wilford near Nottingham.
At a preliminary hearing in Belfast ahead of his inquest later this year, Coroner Patrick McGurgan said relatives should be offered the chance to give evidence.
"I think all efforts need to be made to trace the next of kin," he said.
A lawyer for the Coroners Service said he believed that some relations may live in Northern Ireland.
Mr McGurgan suggested lawyers who represented Black in trials prior to his death might be able to help trace relatives.
"I think it's important that the family are given every opportunity to participate fully in this inquest," he said.
Black was cremated and his ashes were scattered at sea after prison authorities in Northern Ireland revealed no one wanted his remains.
The killer's long reign of terror was ended in 1990 when he was caught red-handed by police with a barely alive six-year-old girl hooded, bound, gagged and stuffed in a sleeping bag in the back of his van in the Scottish village of Stow.
He had sexually assaulted her moments earlier.
Once in custody, the predator was linked to a series of unsolved crimes in the previous decade.
In 1994, Black was found guilty of three child murders in the 1980s - those of Sarah; 11-year-old Susan Maxwell, from the Scottish Borders, and five-year-old Caroline Hogg, from Edinburgh - as well as a failed abduction bid in Nottingham in 1988.
In 2011, he was found guilty of the 1981 murder of nine-year-old Jennifer Cardy, from Ballinderry, Co Antrim.
Black, who lived out his last days in Maghaberry high security prison in Co Antrim, was also suspected of involvement in other killings and unexplained disappearances.
He had long been the prime suspect in the case of missing 13-year-old Genette Tate, who was last seen in a rural lane in Aylesbeare, Devon, in 1978.
The killer was put up to be fostered within weeks of his birth in 1947.
A couple from Kinlochleven in the West Highlands who took him in both died within 11 years and Black spent the rest of his childhood in residential homes in Falkirk and Edinburgh.