Venezuela has been in political turmoil since assembly speaker Juan Guaido declared himself acting president in January in a direct challenge to President Nicolas Maduro's authority.
The NRK radio and television network, quoting anonymous sources, said peace talks have taken place at a secret location in the Norwegian capital for "several days" and are expected to conclude on Thursday,
It is the second time that such talks have been held in Oslo between Maduro's regime and Guaido's representatives, NRK said.
It said negotiations have also taken place in Cuba.
"We can neither confirm nor deny Norway's involvement in peace processes or dialogue initiatives," a Norwegian foreign ministry spokeswoman, Ane Haavardsdatter Lunde, told AFP.
Venezuelan Communications Minister Jorge Rodriguez and the governor of Miranda province Hector Rodriguez represented Maduro's government, NRK said.
The opposition is represented by former deputy Gerardo Blyde, former minister Fernando Martinez Mottola and the vice president of the National Assembly Stalin Gonzales.
In Caracas, Maduro said Jorge Rodriguez "is overseas, on a very important mission".
Guaido, the leader of Venezuela's opposition-controlled legislature, is locked in a bitter power struggle with Maduro, who has presided over a spiralling political and economic crisis in Venezuela since taking over from late leftist leader Hugo Chavez in 2013.
Maduro was re-elected to a second term in May 2018, in a vote boycotted by the opposition and rejected by much of the international community.
Guaido declared himself acting president on January 23, calling Maduro's re-election illegitimate. The opposition leader has since been recognised by more than 50 countries, led by the United States.
Norway however has merely called for new free elections in Venezuela, a position seen as illustrating a willingness to act as a mediator between the two sides.
At the end of January, Norwegian Foreign Minister Ine Eriksen Soreide said her country was "ready to contribute if and when the parties so wish".