The Norwegian Directorate of Immigration told NRK that persons with legal residence in Russia are likely to be returned there.
Tor Espen Haga of the National Police Immigration Service said this was likely to include many of those coming over the Arctic border at Storskog.
At Fjellhallen transit center in Kirkenes, NRK journalists spoke to many refugees who had lived a long time in Russia, often years, and who had received work or student visas.
The number of refugees entering Norway through the Storskog border crossing near Kirkenes has shot up this year, with more than 500 arriving this year.
Many of the refugees have made the crossing on bicycles, as it is illegal to cross on foot according to Russian border regulations.
However, some of the refugees complained that conditions in Russia were harsh for Syrians, with little chance of making a living.
"Russia doesn't give us anything. If they catch you working, they throw you in prison," Khalil, a 23-year-old Syrian refugee told NRK. "You can stay in Russia, but you are not allowed to work or do anything."