Brady’s lawyer Giovanni di Stefano said his client’s request had been inspired by the release of the Lockerbie bomber Abdelbaset Ali Mohmed Al Megrahi on compassionate grounds.
Brady, 71, who was born in Glasgow, has said he wants to die and is being force-fed following a series of hunger strikes.
Mr Di Stefano said: “There is no reason Brady should not return to his own country just like Mr Al Megrahi did.
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“The attitude regarding mental health in Scotland is perhaps somewhat diverse to the UK, and I have told Brady that he may well achieve his goal by being transferred there.”
He said all Brady wanted was to move to a prison and be allowed to die.
He is currently being held in Ashworth High Security Hospital, Merseyside.
Mr Di Stefano hopes to have Brady moved under the Repatriation of Prisoners Act 1984.
Brady was jailed alongside Myra Hindley in 1966 for murdering five children in the Manchester area in the 1960s.