During his trial last year, friends of the far-Right extremist pointed to his decision to drop out of high school before graduating, despite higher than average grades, as a key turning point in his pathway to extremism.
Knut Bjarkeid, the director at Ila Prison, where Breivik is serving a 21-year sentence, said he would encourage such a move.
"The prison will always try to pave the way for inmates to get a formal education, so that they are able to get a job when they come out," he told Norway's TV 2 channel.
However, several members of teaching staff at the department of Political Science, who wished to remain anonymous, told the channel that they would refuse to teach the far-Right extremist.
Ole Petter Ottersen, the University's Rector, said: "I understand that there will be reactions. It is human."
But he explained that the University would assess Breivik's application on its own merits.
"We cannot refuse anyone the chance of studying at the University of Oslo," he said. "We have to follow the technical rules for admission."
Thomas Hylland Eriksen, a professor of Social Anthropology at the University, who Breivik demonises as a leading "cultural marxist", said he believed the terrorist should be allowed to study.
"It is Breivik's right to get an education just like everybody else's, but that it should by no means be obvious that he should be allowed to leave the prison where he is incarcerated in order to attend lectures," he said.
Breivik killed 77 people and wounded 242 others when he detonated a bomb in central Oslo and then opened fire at a Labour party youth camp in July 2011.