The American request, confirmed in a statement from the commanding officer of Marine forces in Europe, comes as tensions between the US and Russia are increasing amid the humanitarian disaster in Syria and US assertions of Russian involvement in cyber hacks on American political organizations and individuals.
"We enjoy a very close relationship with the Norwegian Armed Forces and a limited rotational presence in Norway would certainly enhance this relationship and our ability to operate together," Maj. Gen. Niel E. Nelson, commander of US Marine Corps Forces Europe and Africa, said in a statement to CNN.
"If approved by the Norwegian government, a Marine Corps presence in Norway will increase NATO's ability to rapidly aggregate and employ forces in northern Europe," the statement continued.
The story was reported earlier by the Marine Corps Times and Military.com.
Tensions about Russia's posture in Europe have increased following the Russian annexation of Crimea in 2014, following Putin's intervention in eastern Ukraine.
The US and its NATO allies have since increased their presence, as well as assistance to Poland and the countries on the Baltic Sea.
Earlier this year, members of the 2nd Marine Expeditionary Brigade trained in Norway alongside troops from other NATO countries in Exercise Cold Response.
The Norwegian government is currently reviewing the US proposal. "We still need to let the Norwegian government make this decision before discussing any details," Nelson said.
Lars Gjemble, a spokesman for the Norwegian Defense Ministry, said in a statement, "The Unites States is a long-term and close ally to Norway. US participation in military exercises and training in Norway is one element in this long-standing and close security policy relationship. Considerations about how to tailor allied exercise activity in Norway is a continuous effort. A limited rotational US Marine Corps presence in Norway is a possible option currently being considered. Even though dialogue has been ongoing at the military level, the process at the political level is still ongoing, and at this time it would be premature to discuss the possible implementation of such an activity."