"I would guide very strongly against that," Cameron told lawmakers in parliament at the weekly Prime Minister's Questions, just before leaving for Iceland to attend the Northern Future Forum.
"Norway actually pays as much per head to the EU as we do, they actually take twice as many, per head, migrants as we do in this country, but of course they have no seat at the table, no ability to negotiate."
Norway is not a member of the European Union but is part of the European Economic Area, which includes Iceland, Liechtenstein and Switzerland.
Some Eurosceptics want Britain to leave the EU and negotiate similar economic agreements with the 29-nation bloc.
Ahead of Cameron's trip to Iceland, the Daily Telegraph quoted a Downing Street source as saying that Britain being outside the EU would not be "a land of milk and honey".
"People need to understand that there are significant downsides," the source said.
Cameron has promised to hold a referendum on EU membership before the end of 2017 and has said he will campaign to stay if he can obtain reforms that would loosen Britain's ties with the rest of the European Union.
He has not ruled out supporting a so-called "Brexit" if he cannot come away from the table with what he wants. But the prime minister is increasingly under pressure to clarify his own position as the pro and anti campaigns rev up.
Cameron added that it was "very important in this debate we absolutely are clear about the consequences" of different options for Britain.