Keith Bennett, who disappeared in 1964, is believed to be buried somewhere on Saddleworth Moor in the Manchester area, Britain's The Sun reported Tuesday.
Keith Bennett is the only one of Brady's five victims whose body hasn't been found.
His mother, Winnie Johnson, died last week after having begged Brady for decades to reveal where her son was buried.
The newspaper said it learned of the existence of Brady's 500-page autobiography in a letter the incarcerated 74-year-old wrote to a pen pal.
"It'd be better if he just told Keith's family where he's buried," said the pen pal, who expressed wishes to remain anonymous.
Brady has said the manuscript can't be released until after his death.
Brady and Myra Hindley were convicted in 1966 of killing five children. At least four of the victims had been sexually assaulted.
The crimes were labeled the Moors murders because three of the victims were discovered in graves on Saddleworth Moor.
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