David Coles contends the information should be released because it is important in helping the public understand what happened.
Bourque, 24, of Moncton, was sentenced last month to life in prison with no chance of parole for 75 years for killing three RCMP officers and wounding two others.
It is the longest sentence in Canadian history.
The Crown and Bourque's lawyer have opposed making the sentencing documents available to the media.
But Coles says they should not be sealed.
A hearing is scheduled to be held in Moncton's Court of Queen's Bench at 10 a.m. AT.
Bourque previously pleaded guilty to three counts of first-degree murder and two counts of attempted murder of RCMP officers.
During sentencing, Court of Queen’s Bench Chief Justice David Smith described the case as "one of the most horrific crimes in the history of Canada."
On June 4, Bourque went on a shooting rampage that resulted in a 28-hour lockdown in the northern part of the city and a manhunt by hundreds of officers from across the country.
Smith said the sentence must be proportionate to the gravity of the offence and his main concern was deterrence.
Up until 2011, the maximum sentence a multiple killer could be given in Canada was life in prison with no parole eligibility for 25 years.
In 2011, however, the federal government passed a new law that allows judges to sentence offenders consecutively when convicted of more than one murder.
The RCMP officers who were killed on June 4 were:- Const. Douglas James Larche, 40, from Saint John.
- Const. Dave Joseph Ross, 32, from Victoriaville, Que.
- Const. Fabrice Georges Gevaudan, 45, originally from Boulogne-Billancourt, France.
The RCMP officers who were wounded were:- Const. Éric Stéphane J. Dubois.
- Const. Marie Darlene Goguen.
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