There are fears that Greek banks present in the region will not be able to finance their subsidiaries and some analysts have even expressed worries about withdrawals of funds from Greek banks.
"There are already measures in place [to deal with the effects of potential deleveraging by banks]," Berglof said. "We don't speak about it much but… in these times of crisis one has to understand the importance of financial stability."
"We still think there is a lot of willingness in Europe and some hope that there will be a solution in Greece," he added.
When the first leg of the crisis hit Central and Eastern Europe in 2009, Western banks present in the region and the authorities in the respective countries met in the capital of Austria and created the Vienna Initiative – an agreement meant to deal with the effects of the Lehman Brothers collapse on the CEE region.
Under the Vienna Initiative, Western banks pledged to maintain funds in their Eastern subsidiaries despite the need for capital in the parent banks, to prevent a disorderly outflow of funds from the region.
The Vienna Initiative was successful in ensuring that there was no significant flight of capital from Eastern European countries but, because of the debt crisis in the euro zone, the region has still not recovered and a new initiative, called Vienna 2.0, was launched.
Under Vienna 2.0, Western banks pledged to maintain lending levels in the countries that receive aid from the International Monetary Fund in the region, including Romania.
"Solvency rate. Prudential measures," Romanian central bank governor Mugur Isarescu told CNBC.com when asked about the measures the country takes to protect against a possible spillover effect from the crisis in Greece.
The solvency ratio in Romania's banking system is above 14 percent and local regulators have said the local subsidiaries of Greek banks are well capitalized.
Romania has not seen significant outflows of foreign portfolio capital and no sign of withdrawal of deposits from banks, deputy central bank governor Cristian Popa said.
"I haven't seen any sign of deposit withdrawals. Our concern is to prevent a possible disorderly deleveraging [of foreign banks' subsidiaries in Romania] from taking place in the future, although parent bank exposure to subsidiaries in Romania has so far remained broadly stable."
"What's important is that the deleveraging doesn't become disorderly, excessive or overly rapid."
"Neither the international financial institutions nor the host countries wish to see a situation in which a credit crunch is created [because of deleveraging]," Popa said.
"Loans from foreign banks to their subsidiaries in Romania have not decreased so far. We are concerned about what could happen from now on," he added.
Popa said the country was working with the International Monetary Fund on continuously improving stress test methodologies for the local banks, with Romania now being one of the most advanced EU member states in terms of banking sector stress testing.
The Romanian central bank deputy governor believes that Greece will be able to overcome its crisis and remain in the single currency.