It would be the first time he has spoken publicly for nearly 50 years.
The 75-year-old argues he is no longer mentally ill and should be moved from a high-security hospital to prison.
Brady, along with his accomplice Myra Hindley, tortured and murdered five children aged from 10 to 17, burying some of their victims' bodies on Saddleworth Moor in the Peak District.
The last time Brady was heard in public was in 1966 at Chester Assizes, where he denied the murders.
He was eventually found guilty of three and jailed for life. He and Hindley later confessed to the other two. Hindley died in prison in 2002, aged 60.
Brady has been held in Ashworth Hospital, a high-security psychiatric hospital in Maghull, Merseyside, since 1985.
Brady's legal team say he has a severe personality disorder but is not mentally ill and could be treated in prison rather than hospital.
But staff at Ashworth say he remains a paranoid schizophrenic who should stay at the hospital.
His reasons for wanting to return to prison remain unclear, although it is thought he might try to starve himself to death in prison.
He has been on hunger strike since 1999 but doctors at Ashworth can force-feed Brady through a tube in his nose under mental health law.
On Monday, a nurse told the tribunal that, despite his hunger strike, Brady often took the food made available to him, and he "makes himself toast every morning".
The serial killer looks likely to be the final witness at the tribunal, which is sitting at Ashworth Hospital and will be relayed to the press and public on TV screens at Manchester Civil Justice Centre.
The judgement of the panel will be released at a later date yet to be fixed.