Four of the victims were buried on Saddleworth Moor
The serial killer, 79, who now uses the name Ian Stewart-Brady, last went before the Mental Health Review Tribunal (MHRT) in 2013 and asked for a move to a Scottish prison.
His request was rejected after Ashworth Hospital said he had chronic mental illness and needed continued care at the Merseyside unit.
A further review was due in September last year, but Brady refused to take part because solicitor-advocate Robin Makin, who has represented him for more than 25 years, was denied a legal aid contract.
- Moors Murderer Ian Brady complains about broken bath hoist
- MEAL TICKET: Sick serial killer Ian Brady gets lavish Christmas feast
He is in very poor physical health
Brady and Myra Hindley, who died in prison in 2002, tortured and murdered five children in the 1960s.
Four of the victims were buried on Saddleworth Moor in the south Pennines.
He was jailed for three murders in 1966 and has been at Ashworth since 1985.
Ian Brady suffers from emphysema and has constant oxygen
He and Hindley later confessed to another two murders.
His legal team say he has been bedridden for the last couple of years or so.
"It is probably fair to say that his physical condition will not improve and he is terminally ill.
Get Quotes on Home Insurance
Myra Hindley died in prison in 2002
"He is in very poor physical health – he suffers from emphysema and has constant oxygen and a nebuliser four times a day."
His case at the High Court in London is listed as "Stewart-Brady v Lord Chancellor".
It was triggered when a bid to appoint Mr Makin as Brady's legal representative was blocked because his solicitors' firm, E Rex Makin & Co, is not a member of the Law Society's mental health panel.
Murderers given whole life tariffs Fri, November 25, 2016
The prisoners serving whole life tariffs in the UK.
SWNS.com 1 of 22
Montage of 55 of the whole life tariff prisoners who are currently being held in British prisons. Thomas Mair today joins the most notorious criminals who are destined to spend the rest of their lives behind bars.
Under legal aid rules, only members are entitled to a publicly funded contract in the mental health law category.
It is understood that the Lord Chancellor, Liz Truss, has taken the stance that "lawyer of choice" is not an absolute rule, and believes she would be acting ultra vires, or outside her powers, if she allowed Mr Makin to have the contract.
Brady's legal team is seeking permission to apply for a full judicial review, arguing that the Lord Chancellor should use her powers to "make arrangements" because the Brady case is "totally unique".
Saddleworth Moor in the south Pennines
They say the MHRT and Ashworth regard the case as unique.
They are expected to tell the court that Brady was reluctant to engage with the latest review but was persuaded to by Mr Makin after "making it clear that the only legal representative he would have was Robin Makin".
- REVEALED: Ian Brady's 17-year hunger strike 'is a SHAM'
- Family of victim of Ian Brady said they are 'waiting' for him to die
- Moors murderer reveals he is dying and blasts 'Brexit blockers'