Here, we investigate how likely that is to happen and explore the potential implications for British savers with money in Cypriot banks.
Earlier this week, the Cypriot Government threw out a controversial plan to skim €5.8 billion (£5 billion) from savers' bank accounts in a bid to solve its banking crisis.
However, an alternative solution is yet to be found.
The British Government has therefore flown in €1 million in low-denomination notes to provide cash for 3,000 British service personnel based on the Mediterranean island as a "contingency measure".
Euros could soon be of little use on the island, though, as the likelihood of Cyprus becoming the first country to quit the Eurozone grows.
According to The Guardian, government MP and former finance minister Marios Mavrides raised the prospect earlier this week.
"If we cannot come up with the €5.8bn in a few days then I think we will go to the Cyprus pound," he said.
"That will be the end of Cyprus in the eurozone. We're going to exhaust all other possibilities but what can we do? If we have no other solution we cannot leave the people without money."
Reuters quotes notes from the call as including discussion of the need to "ring-fence" the rest of the Eurozone from the impact should an exit become unavoidable.
This is worrying for anyone with money in Cypriot banks, particularly the numerous Russian nationals reported to have deposited at least €17 million into accounts offering high interest rates and little or no account vetting.
The Ministry of Defence has said that is is "approaching personnel to ask if they want their March, and future months' salaries paid into UK bank accounts, rather than Cypriot accounts".
Any other Brits living in Cyprus may be wise to take similar measures as there are no guarantees at this stage, despite the Cypriot Government promising details of a "Plan B" that it is hoped will leave savers' cash untouched.