The lender, which the State Bank of Vietnam acquired along with two others for zero dong in 2015, announced on Wednesday that interested buyers should submit their plans for restructure by December 16.
Global Petro Commercial Joint Stock Bank, as the bank is formally known, has not published its results for the last three years.
In 2015, the latest year for which data is available, its capital was increased by 30 percent after it was acquired to VND20.9 trillion ($902.8 million).
But it has been struggling to recover bad debts. In 2016 the bank recovered only VND307 billion ($13.3 million), or 15 percent of the target, according to state auditors, who warned it would only be able to recover a maximum of 31.5 percent.
The other two weak banks the government acquired are Vietnam Construction Bank (VNCB) and OceanBank.
Japanese finance firm J Trust in March expressed interest in acquiring VNCB, while the SBV in May proposed to the government to sell OceanBank to an unidentified foreign buyer.
Vietnam caps foreign ownership of banks at 30 percent, but there is no limit for the three weak banks, the government has clarified.