Breivik is in a maximum-security prison for killing 77 people in a terror campaign launched two years ago, Britain's Guardian reported.
His sentence of 21 years, a mandatory initial lenghth under Norwegian law, will be reviewed periodically and can be extended in increments if he is considered a continued threat to society.
Oslo University rector Ole Petter Ottersen confirmed Breivik seeks to study a single topic that would not lead to a degree.
Ottersen declined to provide any details on how Breivik's application would be treated.
"Prison inmates are allowed to study and we have a set of rules that we stick to in assessing applications," he said.
News of Breivik's application drew negative reactions from many staff members.
The University of Oslo is Norway's oldest institution of higher learning. It has five Nobel Prize winners among its alumni.
It's Latin motto is et nos petimus astra (We strive for the stars).