Both US and Russian officials have approached Norway with oral requests for help in dismantling the weapons, Norwegian public broadcaster NRK said on its website.
Both countries consider Norway a suitable location for the dangerous work, as it is politically stable and has large amounts of water, which is needed for the task, according to NRK.
According to UN Security Council Resolution 2118, adopted late last month, Syria has until the end of June 2014 to destroy its chemical weapons.
The Norwegian foreign ministry could not immediately confirm the specific details of the report, but said the Scandinavian nation stood ready to assist.
"I can confirm that Norway is looking into implementing the resolution of the UN Security Council," ministry spokesperson Ragnhild Imerslund told AFP.
"Exactly how it will be done is too early to say. We don't know what contribution we are going to make, but we are looking into various options."
Norway has until the middle of November to come up with a reply to the request reportedly made by US and Russia, according to NRK.
Most likely the decision will be made by Norway's incoming centre-right government expected to assume power on , following an election victory last month.
Norway currently does not have the equipment necessary for destroying chemical weapons, but the United States may offer mobile facilities to help in implementing the task, NRK said.