Building the new headquarters is expected to cost between 8 billion and 10 billion kroner ($1.35-$1.69 billion), Government Administration Minister Rigmor Aasrud told TV 2.
"These are just rough estimates for now," she said.
The new building is not expected to be completed before the early 2020s.
"It normally takes between eight and ten years to carry out such big projects," Aasrud said.
The government is to announce next year whether it will partially or completely tear down or repair the 17-storey building that houses the office of Prime Minister Jens Stoltenberg and which was heavily damaged in the July 22nd 2011 blast.
Breivik took advantage of lax security outside the building and parked a van loaded with explosives at the foot of the office block, setting off a bomb that killed eight people.
The 33-year-old right-wing extremist then went to the island of Utøya, some 40 kilometers outside of Oslo, where he spent more than an hour gunning down 69 people attending a Labour Party youth camp.
Breivik has been charged with "acts of terror" and an Oslo district court is due to announce its verdict on Friday.