The State Bank of Vietnam said it has presented the proposal to the government, but did not disclose the name of any prospective buyer.
In 2015 it acquired OceanBank and two other struggling banks for zero dong.
Deputy Prime Minister Vuong Dinh Hue had said last year that the government would allow foreign investors to fully acquire these weak banks, Vietnam Construction Bank and Global Petro Commercial Jsc Bank being the other two.
Under the law, foreign ownership at local banks is capped at 30 percent, except for the "weak banks".
The SBV had said in 2017 that an Asian bank "expressed serious interest in restructuring OceanBank" and was taking "necessary steps."
Last March Japanese finance firm J Trust expressed interest in acquiring and restructuring the Vietnam Construction Bank.
Vietnam has nine foreign banks, four state-owned banks and 31 joint-stock banks.