In the past few weeks chief economists from the French Central Bank, the International Monetary Fund and the European Central Bank have indicated that a bank union could be a good solution.
This autumn the EU Commission will present a proposal for a common banking system, shared control mechanisms and a deposit guarantee that would be financed by all of the EU countries.
A common banking system would also benefit Sweden, according to Erik Berglöf, chief economist of the European Development Bank.
"We are affected by the same problems, and a collapse of the euro system would hit Sweden very hard," Berglöf told Swedish Radio News.
But Mats Persson, a professor of international economics at Stockholm University disagrees.
"Sweden doesn't need a bank union. Sweden is stable with a well-functioning financial inspectorate. Countries that do not manage their financial affairs want a common banking system, so they can get money from the countries that do manage well," Persson said.