None of the company’s seven board members are among the 13 who have offered to resign, Bloomberg reported, citing a company statement.
One of the resignation letters came from Ko Jae-ho, the former chief executive, according to IHS Maritime.
IHS also said Daewoo plans to accept voluntary resignations and could reduce more senior staff by the end of the month.
Daewoo said last week that it will sell non-core subsidiaries and assets and shut down or exit non-essential units to focus on improving competitiveness in its shipbuilding operations, according to reports.
Among the assets reportedly up for sale is a partial stake in a Chinese shipyard where it makes components for vessels. Daewoo also indicated that it would sell the company headquarters in Seoul.
Daewoo’s non-core businesses accounted for about 10% of the company’s revenue in 2014, according to Reuters.
The restructuring plan was announced after the company reported a 2.4 trillion won ($2 billion) loss in the second quarter.
The losses were attributed to delays in completing four oil rigs ordered from Songa Offshore.