The defense ministry in Oslo said Monday, Censor.NET reports citing The Daily Star.
"Assessments have taken place within the military to look at the options for additional training, storage and this kind of thing," ministry spokesman Ann Kristin Salbuvik told AFP, saying this was a "long-standing U.S. wish."
"It may be something that is carried out on a rotational basis... (but) there is no question of permanent deployment," she said.
Salbuvik stressed that ideas were still at an early stage and were being conducted by the two militaries and had not been broached at a political level.
The Norwegian newspaper Adresseavisen Monday said the Pentagon wanted to station 300 U.S. Marines at Vaernes, near the western city of Trondheim, about 1,000 kilometers (600 miles) from the Russian-Norwegian frontier.
Norway and Russia share a 200-km border in the Arctic Circle.
Norway became one of NATO's founding members in 1949, but - in response to Soviet fears - promised not to let foreign combat forces deploy on its territory as long as the country was not under attack or threatened with attack.
The commitment was subsequently revised so that foreign troops could carry out exercises on Norwegian soil.