The move follows Brooks' failed application for core participant status in September 2011Credit: PA Wire
In September Lord Justice Leveson refused an application to grant the former News International chief executive the status, which allows participants to be legally represented at the inquiry and have questions asked on their behalf.
Stephen Parkinson, acting for Brooks, said today she "may be someone who will be the subject of explicit criticism".
He said one of the reasons for applying for the status was to receive advanced notice of evidence and to put questions to those called to give evidence.
Lord Leveson said that he would reply to the application in writing "I hope in the course of the next few days", signalling that he would do so before Easter.
He also set out the timetable for the next few months.
The inquiry will not sit the week beginning 16 April.
The following week, beginning 23 April, will see him "calling newspaper proprietors or media owners and other evidence crossing modules".
Module three, focusing on the relationship between the press and politicians, will start after local elections are held in early May and will run to the end of June.
Module four, which will look at "recommendations for a more effective policy and regulation that supports the integrity and freedom of the press while encouraging the highest ethical standards" will commence in early July.
Lord Leveson expects to complete the "formal part of the inquiry" by the end of July, "before the anniversary date of the appointment of this inquiry".