A specialist team will hunt for the remains of the 12-year-old and those of three other missing children whose bodies were buried on Saddleworth Moor near Manchester in the 1960s by Ian Brady and Myra Hindley, according to the Daily Mirror.
The newspaper said new research by a consortium of lawyers, former police officers and a High Court judge investigating the Moors murders would be made public in the coming days with "fresh facts" that they hope will lead to finding the bodies.
Welsh mountain rescue leader David Jones visited the moor with Keith's mother Winnie Johnson four years ago, when he identified 19 areas of interest.
Mrs Johnson made repeated calls for Brady to reveal the location of her son's grave, but died in August 2012 without being able to fulfil her last wish of giving her son a proper burial.
Mr Jones said new evidence had reduced the search to an area the size of three football pitches that he will now search using specialist equipment and sniffer dogs.
He told the Mirror he believes the evidence will bring them closer than "anyone has ever got" to finding the missing children's remains, saying his priority is to find Keith.
He said: "I am hoping 100% that we can find Keith, but I am aware that it might not be him buried. We've identified three specific new areas of the moor and will operate a grid system of search using the equipment and dogs."
A spokesman for the project told the newspaper that the team felt they were getting "very close" to resolving the case, and that a large team including scientists had been working to discover why Keith's body has never been found.
In a separate development, Keith's brother Alan said that he had also obtained new evidence that may identify where the body was buried, including maps, diagrams, witness statements and taped interviews with Hindley's brother-in-law, David Smith, before he died.
He told the Mirror that a "credible new witness" who has corresponded with Brady was asked by the jailed killer to take photos of certain areas of the moors, areas that he said "mirrors information given to us by David Smith".
He said : "My hopes are to have another search of the precise area where we believe Keith is."
Brady and his partner Hindley murdered five youngsters in the 1960s, luring the children and teenagers to their deaths and sexually torturing them before burying them on Saddleworth Moor.
Pauline Reade, 16, disappeared on her way to a disco on July 12, 1963 and John Kilbride, 12, was snatched in November the same year.
Keith Bennett was taken on June 16, 1964 after he left home to visit his grandmother; Lesley Ann Downey, 10, was lured away from a funfair on Boxing Day 1964; and Edward Evans, 17, was killed in October 1965.
Brady was jailed for life in 1966 for the murders of John, Lesley Ann and Edward. Hindley was convicted of killing Lesley Ann and Edward and shielding Brady after John's murder, and also given a life sentence. In 1987 the pair finally admitted killing Keith and Pauline.
Hindley died in jail in November 2002 aged 60, while Brady is held at the high-security Ashworth Hospital in Merseyside.