European leaders have given Greece until the weekend to reach an aid-for-reforms deal with its creditors or risk bankruptcy and banking collapse. Here, we outline the currency options available to Greece if it leaves the single currency.
Keep the euro
Greece could unilaterally "adopt" the euro, even if it left the euro zone. This option would see it join countries like Monaco, Andorra, San Marino and Vatican City which all use the euro as their national currency, despite not being euro zone member states.
The European Commission, the European Union's executive arm, allows these countries to issue limited amounts of euro coins, but they're not allowed to print their own banknotes. Only the European Central Bank (ECB) can authorise the issuing of issue euro banknotes.
Greece would likely be required to pay its debt to the ECB in order to qualify, and the central bank would need to be in a "mood" to carry on providing assistance to the country's banks, Jane Foley, a senior currency strategist at Rabobank, told CNBC.
Develop a parallel currency
If the ECB stops providing Greek banks with emergency funding, the central bank could begin printing another currency without giving up the euro to meet its commitments, such as welfare payments. The value of the new currency could likely fall rapidly against the euro, which could seriously impact Greeks' spending power.
This inflation would give Greeks an incentive to carry on using the euro, Foley explained, entrenching a dual currency. It could effectively create a two-speed economy, with the euro dominating in sectors like tourism.
Read MoreWhy the drachmacan't save Greece: Goldman
Roger Bootle, executive chairman of Capital Economics, told CNBC that a parallel currency—rather than replacing the euro altogether—would be a way for Greece to show Europe that it hadn't left the currency union. This could potentially make it easier to continue to receive financial aid.
"It's a fudge," Bootle said. "It's an awkward half-way house."
Return to the drachma
Another option is for the country to revert to its pre-2001 currency, the drachma, leaving the euro behind altogether.
"The key thing is that it has to redenominate deposits and debts into a new currency ... which is the easy thing to do," Bootle said. "The trickier thing to do is in terms of supplying notes—initially there won't be any notes available."
To deal with what's bound to be a "messy situation," the government might issue IOUs in the interim. Stamps, for example, could be quickly printed in large volumes and used in place of bills, Bootle explained.
Adoption of any new currency—whether or not it's called the drachma—would result in further defaults, Foley said. Greece has already effectively defaulted on a 1.5-billion euro ($1.6 billion) payment to one of its biggest creditors, the International Monetary Fund.
A new currency would inevitably be weaker than the euro, increasing the weight of the country's euro-denominated debt.
"Greece needs to be able to issue their own currency and need[s] the devaluation that comes with running your own currency," Bootle said. It's unlikely to be an easy transition, but he insisted that this was the country's best option.
Pegged currency
Many countries regulate their currencies by linking them to the euro. Adopting a pegged currency, however, requires either a stable economy able to ward off speculative attack, or significant currency reserves.
Bulgaria had enough reserves to introduce what's known as a currency board. This means it is committed to converting its currency—the lev—for euros on demand. However, Greece is unlikely to drum up enough currency stockpiles to use this option.
Denmark's currency, on the other hand, is pegged to the euro but its economy is considered strong enough to maintain the peg without needing to build up such currency stores.
Digital currency
Some have suggested that Greece could adopt a digital currency like bitcoin, avoiding the messy practicalities of a new currency or paper IOUs.
Garrick Hileman, an economic historian at the London School of Economics, said that while it's "very unlikely" that the Greek government would formally adopt bitcoin as an official currency, its use may increase significantly in the event of a Grexit.
"Greeks may understandably lack confidence in a new drachma and seek an alternative," he said.
But both Bootle and Foley were skeptical that an economy that relies so heavily on cash could function without physical bills.
Read MoreGrexit to drachmawould be dangerous: Larry Summers
"It's more likely Greece would completely revert to cash, which is already happening, than digital currency," Foley said.
She said that although digital transactions still appeared to be working in Greece, "if you're a small producer, you're probably going to prefer to see the cash given the uncertainties."
Indeed, rather than look to digital currencies, Bootle said that people get creative in finding ways of dealing with a limited amount of bills. Old-school trade dynamics could come into play, for example, with consumer goods like cigarettes used in place of currency.
"There's all sorts of ways that people will find a way around it," he added.