Reforms which came into force on Thursday mean Parole Board hearings can be opened up to victims and the press as the Ministry of Justice wants to make the process more transparent.
The prisoners, government ministers and officials are also among those who can request that the case is not discussed behind closed doors.
Bronson, one of the UK's longest-serving inmates who has since changed his name to Salvador, was widely expected to request his latest parole hearing be heard in public, having previously said he wanted his to be the first to take place.
The Parole Board confirmed on Thursday it had received a request for Bronson's case to be heard in public and it will now be considered.
It is understood the application was made on his behalf.
Review may take place this year
A date has not yet been set for his next review, although it is thought this may take place 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.
Bronson was given a seven-year sentence for armed robbery in 1974, but was returned to prison after his release after he was found plotting another offence.
He is serving a life sentence that he was given in 1999 after he held a visiting teacher hostage at knife point. Much of his time has been spent in solitary confinement.