Norway has set up a group of experts to study the proposal, which came last month after a UN resolution compelling Syria to dismantle its chemical arsenal by mid-2014.
"We are taking this request from the US very seriously," Brende said during a meeting with foreign correspondents in Oslo, barely a week after taking office.
Those chemical weapons which are armed and ready to use would most likely be destroyed in Syria but chemical components still not assembled could be taken out of the country and destroyed elsewhere.
Norway has been asked to destroy between 300 and 500 tonnes of sarin and up to 50 tonnes of mustard gas, according to UN sources cited by Norwegian public service broadcaster NRK.
Brende refused to comment on the figures as he said UN weapons inspectors still have to complete their assessment.
The Organisation for the Prohibition of Chemical Weapons, which won this year's Nobel Peace Prize, has been inspecting chemical weapons production and storage sites in Syria since the beginning of October.
"We do not have the expertise in this field (of destroying chemical components) and we do not have the equipment," Brende said, pointing at the
need for another country, like the US, to provide it.
One of the conditions cited by Oslo for a positive response is that the waste created by the process would be sent to another country, since Norway does not have storage facilities for toxic organic waste.
"I do not think that is a major obstacle," he said pointing to other more important issues such as the low temperatures in Norway, which can freeze the
water needed in the destruction process.
Brende said Norway will respond "as soon as possible" once it has gathered all relevant information.