Cameron infuriated other European Union members last month and sparked speculation about Britain's place in the bloc it joined in 1973 by blocking an EU treaty change and forcing eurozone countries to negotiate a fiscal accord outside the Union.
All EU countries other than Britain now plan to sign a treaty outside the full EU framework at a summit on Monday.
But Cameron said he had not seen a shift in position by other EU countries that would allow Britain to sign a treaty with them.
"I haven't seen that movement because the conditions we set out are the conditions we set out and they haven't been moved towards so I don't see that development," he said in an interview with CNN at the Davos Forum.
Britain had asked last month for safeguards around the single market for financial services but had not got them "so we can't have a treaty inside the European Union," he added.
Those EU countries that had not joined the single currency have been "frankly out of the room when the eurozone issues are discussed," Cameron said. "But I think we should take a relaxed view about that."
"Britain gets a lot out of Europe through the single market, through our engagement on foreign affairs and other issues but we don't want to be in the euro zone."
Turning to the British economy, Cameron said Britain needed to show the world it was dealing with its debt, adding that its efforts to do so allowed the country to have low interest rates.
"If you took your foot off the pedal and you eased up and spent some more money, borrowed some more money in a discretionary sense, you could lose all the benefit of that by those interest rates going up," he said.
"These are tough times and we have to take bold measures."