"There's nowhere in the world that has a single currency without having more of a single government," Cameron told Britain's Daily Mail.
"Making sense of the euro for me would mean that those euro zone countries would have to have much more co-ordinated economic policy, much more co-ordinated debt policy," he said.
Cameron, who opted out of a new European economic pact late last year, advocated Britain's position outside the euro and its ability "to do things to ourselves, for ourselves, by ourselves.
"I have always believed different countries at times will need different economic policies, interest rates tailored to their own needs."
Cameron said, however, that it is in Britain's interest to see a return to growth in the euro zone, which accounts for 40 percent of UK exports.
"We want them to sort out the problems that they have. We want to be in the single market, we want European co-operation, we don't want to be in the euro," Cameron said.
"The euro is a project in transition that could go in a number of different ways ... all these countries have to make their own choices."
(Reporting by Stephen Mangan; editing by Christopher Wilson)
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