Devon and Cornwall Police said a dossier on the Scottish-born sex attacker, who died in January, had been handed to the Crown Prosecution Service (CPS) in connection with the death of 13-year-old Genette Tate.
Genette vanished from a rural lane in Aylesbeare, Devon, in 1978. Her body has never been found.
Black, 68, was serving multiple life sentences for the murders of four schoolgirls in the 1980s and a number of other crimes when he died in non-suspicious circumstances in Maghaberry jail in Northern Ireland.
A senior police source told the BBC a “clear statement” from the CPS about charging Black was the closest Genette’s family would now get to justice.
A spokesman for Devon and Cornwall Police said: “The major part of a file concerning this matter has now been sent to the CPS for a charging decision. We now await further direction from the CPS on how this may progress in the coming weeks.”
Earlier this year, police said they were “weeks away” from charging Black with Genette’s abduction and murder when he died.
Detectives are said to have found two new witnesses following a re-investigation of the case.
In 1994, Black was found guilty of three child murders in the 1980s - those of 11-year-old Susan Maxwell, from the Borders, five-year-old Caroline Hogg, from Edinburgh, and Sarah Harper, 10, from Morley near Leeds - as well as a failed abduction bid in Notingham in 1988.
In 2011, he was found guilty of the 1981 murder of nine-year-old Jennifer Cardy, from Ballinderry, Co Antrim.