Greek stocks soared 7% on Tuesday after reports emerged that Athens had delivered its list of economic reforms to the European Commission.
Eurozone finance ministers will discuss the reforms on Tuesday, while the list will require the full approval of the European Commission, European Central Bank and the International Monetary Fund, known as the troika.
The reform proposals are thought to include measures to combat smuggling and tax evasion, along with increased social spending.
If the measures are approved, Greece would gain access to four-months of financial assistance, during which time Athens is hoping to renegotiate its long-term agreement with creditors.
Greece's hard left government won power on the back of pledges to reform the country's relationship with its creditors, who the majority of Greeks blame for strangling the Greek economy through strict austerity measures.
Uncertainty over Greece's future within the eurozone has sent shockwaves through the country's private banking sector.
Deposit outflows reached €1bn in one day
Deposit outflows reached €3bn (£2.19bn) last week, as the Greek government struggled to negotiate an extension of its bailout agreement, according to JP Morgan bank.
Money started pouring out of private banks in January after the hard left Syriza party won elections and became the dominant party in the governing coalition. Outflows have since accelerated as Greece's future within the eurozone became increasingly precarious.
The vast outflow was a 50% hike on total outflows in the previous week, which reached €2bn. If outflows were to continue at such a speed, Greek banks would be on track to run out of collateral for new loans in just eight weeks, JP Morgan said.
Outflows reached €1bn over Wednesday and Thursday, while Friday alone saw €1bn of outflows from Greek private banks.
"The agreement is likely to decelerate the pace of deposit outflows seen since Syriza gained power," IHS senior economist Diego Iscaro said in a statement.
"However, deposits are unlikely to return to their pre-January level given that uncertainty regarding the ability of Greece to reach a permanent deal with its creditors in June is still high."
If Greece manages to secure a deal, relief would only be temporary. Another round of uncertainty awaits in June, when the same players will reconvene and the possibility of a Grexit would once again destabilise the Greek and European economies.