The daily newspaper Verdens Gang reported on its website that none of Norway's existing mental facilities are considered secure enough to house Breivik, whose sanity is the key focus of his ongoing trial.
If Breivik is found insane, he would be committed to the new facility at the prison in Ila, where he is already being housed during his trial.
"We are building a high-security hospital in Ila," deputy health minister Robin Koss told the newspaper, adding the facility near Oslo still needed state certification.
Breivik, a right-wing extremist, wants to prove he is sane because he thinks people may give his views more weight and not simply dismiss them as the rantings of a madman.
If he is found sane, he would likely face Norway's maximum 21-year prison sentence, which can be extended for as long as he is considered a threat to society.
The 33-year-old admitted to killing 77 people in a July 22nd bomb attack and shooting rampage.
Oslo judges have said they will likely hand down their verdict on either July 20th or August 24th.