The IFC board will discuss the proposition in June.
Banca Romaneasca is 89.1% owned by the National Bank of Greece, while the European Bank for Reconstruction and Development holds a 10.1% stake.
NBG posted a net profit of EUR12 million in Romania last year, down 37% from EUR20 million in 2009.
Banca Romaneasca has a nationwide network of 146 units and some 1,500 employees.
IFC is the investment division of the World Bank Group.