The Prime Minister told Radio 4's Today programme that Greece's referendum on austerity proposals, due to take place on July 5, should determine whether the country keeps the single currency.
Meanwhile, Mr Cameron has chaired a top-level meeting to prepare a "contingency" plan for the fall-out of events in Greece to mitigate the impact on expats and the British economy.
Greece must repay €1.6billion (£1.1billion) to the International Monetary Fund (IMF) before 30 June.
But the Greek government announced the snap referendum on the terms put forward by the country's creditors.
Asked whether the referendum called by Greek prime minister Alexis Tsipras amounted to an "in/out" vote on remaining in the eurozone, Cameron told Today: "I think that's what it will come down to.
"If the Greek people vote 'yes', they are voting for the sort of deal that was put forward by the institutions and therefore voting to have that as an option.
"If they vote 'no', I find it hard to see how that is consistent with staying in the euro, because I think there would be a very significant default and a very significant problem. But it is for the Greek people to decide."
David Cameron says if Greece votes 'no' to bailout terms, they should leave the euro
Ahead the Prime Minister giving a statement to the Commons, his official spokesman said Mr Cameron chaired a meeting with Chancellor George Osborne and other Cabinet minsters over the impact of the crisis on holidaymakers, expats and the UK economy. Bank of England governor Mark Carney was also expected to attend
While contingency planning meetings have already taken place, it was the first to include the top names on the economy. "Given the situation, this is the appropriate people to meet on this occasion," the spokesman said.
Cameron's comments come after the European Central Bank (ECB) announced it would provide an emergency credit line to Greek banks after customers queued for hours to withdraw cash.
The country's banks are to remain closed in the week leading up to the bailout referendum.
Cameron said that the British government is preparing for "every eventuality", whatever the referendum result.
He said that Britain's interest was in a stable and secure eurozone and an EU with the flexibility to deal with the issues facing different countries - including the concerns which prompted him to call a referendum in the UK on the country's membership.
Greece's finance minister had earlier said there was "absolutely no reason" that a Grexit was inevitable and a 'no' vote in the poll "doesn't have to and it shouldn't" mean the country ends up leaving the single currency.
Yanis Varoufakis said there are 'no provisions' for leaving the Euro
Yanis Varoufakis told Radio Four on Sunday: "There are no provisions for leaving the euro. Once in, you can't get out. This is part of the European Union treaties. And why should we have to consider even getting out of the euro?"
The Greek minister also said that he found it "appalling" that the prospect of the ECB turning off the tap was even being discussed and insisted such a move would show Europe had "failed in its duty" to preserve the monetary union.
Eurozone ministers have criticised Greek prime minister Alexis Tsipras for announcing a referendum would be held next Sunday on the bailout proposals.
In a meeting later today, Cameron will ensure that the "final touches" have been put to government plans to assist British holidaymakers and ex-pats in Greece, and to protect wider UK interests, in the case of a default by Athens.