The authority wants banks to boost their reserve in order to protect them from any future shocks in the financial markets.
It is expected governments may have to provide some of the funds, the BBC reported.
The EBA want the banks to up their reserve holdings to between 9% and 10% of their overall assets, after allowing for reductions in the value of their loans to Greece, the Irish Republic, Portugal, Spain and Italy.
The French government had insisted the new money should be provided from the eurozone bailout fund, the European Financial Stability Facility.
However German ministers argued this would put too much strain on the German public sector balance sheet and said the governments of richer countries, such as France, should provide the capital.