The paedophile and child killer died of a chest infection and pneumonia on Monday at a secure hospital in Merseyside. He was 79.
Along with Myra Hindley, who died in 2002, he killed five children between 1963 and 1965, abducting them before sexually assaulting and murdering them.
On Thursday, Brady’s body was released to his lawyer and it had been reported that he wished to have his remains burnt and ashes scattered in the city where he grew up.
Glasgow City Council said it would not allow him to be cremated in the area.
A spokesman said: “We have not had such a request but we would refuse that request.
“We would advise the private crematoria not to accept the request or any such request, should it be forthcoming.”
Brady and Hindley’s victims – Pauline Reade, John Kilbride, Keith Bennett, Lesley Ann Downey and Edward Evans – were aged between 10 and 17.
The couple were jailed for life for three of the killings before later admitting the murders of Pauline and Keith.
Fifty years on, the remains of 12-year-old Keith have never been found – despite the belief that Brady knew the location and buried him on the Moors, where he buried three others.
At an inquest on Tuesday, Senior Coroner for Sefton, Christopher Sumner, had delayed the release of the body to ask for assurances that a funeral director and crematorium willing to take it had been found.
He also wanted a guarantee that Brady’s ashes would not be scattered on Saddleworth Moor.
At a reconvened hearing on Wednesday, Brady’s solicitor, Robin Makin, said there was “no likelihood” the ashes would be brought there.
Mr Sumner delayed the body’s release further to allow Merseyside Police to negotiate with Mr Makin about arrangements for the funeral.
The full inquest into Brady’s death will take place on 29 June.
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