The unsurprising announcement comes as the bank, which has suffered badly from losses on mortgages it had made, continues to stumble.

Shares in Washington Mutual fell nearly 10 percent on Wednesday to $2.09; they have plunged 94 percent over the last 12 months. This week alone, investors have been frightened by Standard & Poor’s cutting of the bank’s debt rating to junk.

Goldman Sachs, which Washington Mutual has hired, started the auction several days ago, these people said.

Among the potential bidders that Goldman has talked to are Wells Fargo, JPMorgan Chase and HSBC.