Reforms came into force on Thursday meaning parole hearings can take place in public for the first time.
This will allow case reviews – which determine if an inmate should be freed from jail or stay behind bars – to be opened up to victims and the press.
The prisoners in question, government ministers and officials are also among those who can request the case is not discussed behind closed doors.
Bronson, one of the UK’s longest serving and most notorious prisoners, had been widely expected to request his latest parole hearing in public, having previously said he wanted to be the first.
The Parole Board confirmed on Thursday that a request for Bronson’s case to be heard in public has been received and will be considered. It is understood the application was made on his behalf.
A date has not been set for his next parole review, although it is thought it could be later this year or early in 2023.
It is not known how long it will take for the Parole Board to decide whether the hearing can be held in public.
Dubbed one of Britain’s most violent offenders, Bronson – who changed his surname to Salvador in 2014 after the artist Salvador Dali – has been in prison for much of the last 50 years, often spending time in solitary confinement or specialist units.
It is believed he is still being held at high-security HMP Woodhill in Milton Keynes.
He previously told how he was first sent to jail in 1968 and has held 11 hostages in nine different sieges in that time – with victims including governors, doctors, staff and, on one occasion, his own solicitor.
Bronson was sentenced in 2000 to a discretionary life term with a minimum of four years for taking a prison teacher at HMP Hull hostage for 44 hours. Since then the Parole Board has repeatedly refused to direct his release.
Earlier this week, the 70-year-old sent a voice message to Sky News from behind bars asking why he was still in jail.
The number of hearings where the overhaul of procedures applies may be limited at first as the criteria require them to remain private unless parole bosses deem it is in the “interest of justice” to open up the sessions.
It is important to state that the normal position will be for parole hearings to remain in private
In deciding whether to grant a public hearing, the board’s chairman could consider factors including the wishes of victims and their families as well as any “undue emotional stress” this could have on prisoners.
Separate rule changes introduced at the same time have stripped officials of their ability to give views or make recommendations to the Parole Board on whether prisoners they work with are suitable for release or transfer to open prison.
Instead, the Justice Secretary will pick cases where they want to make recommendations, having sought advice from officials.
This is known as providing a “single view” representing the Ministry of Justice’s (MoJ) position. Officials will provide factual information such as details of offending and risk management plans which present an “evidence-based assessment of the risk the prisoner presents”.
A Parole Board spokeswoman said: “The new Parole Board rules make it possible for parole hearings to be held in public for the first time in some cases where it is in the interest of justice to do so.
“It is important to state that the normal position will be for parole hearings to remain in private to ensure that witnesses are able to give their best evidence and that victims are not put in a position that could lead to re-traumatisation.”