Geir Lippestad - Håkon Mosvold Larsen/Scanpix
According to the broadcaster, the party leadership is looking for a candidate with broad appeal who has a chance of unseating the current mayor Fabian Stang, and the Conservatives, who have controlled the city since 1995.
"Geir Lippestad is a man who enjoys enormous respect among people. He is one of very few that have the potential to become a real challenger to Fabian Stang," said NRK's source, described as a "central Labour party figure".
"We must have a mayoral candidate who can match Fabian Stang's popularity and the people he has with him," Jan Bohler, the Labour party's leader in Oslo, told NRK. "He or she must be popular on a separate basis, and not a copy of Fabian Stang."
Lippestad would not discuss his possible candidacy.
"I have never been asked, so I have never had the opportunity to decide," he said. "This is a purely hypothetical question."