(Corrects paragraph 4 to read 7.7 billion instead of 7.7 million)

The U.S. Treasury Department is talking to Citigroup Inc about how to sell the roughly one-third stake the government acquired as part of its bailout of the bank, Bloomberg reported, citing people familiar with the matter.

The Treasury may start unloading shares as soon as October, and would aim to sell the holdings over the next six to eight months, the newswire reported, citing one of the people familiar with the matter.

Shannon Bell, a spokeswoman for Citigroup, declined to comment.

The U.S. government has about 7.7 billion Citi shares, representing 33.6 percent of the company's outstanding stock.

Citigroup has recorded more than $100 billion of writedowns and credit costs since the financial crisis began, as it wrestles with bad loans to consumers. The government gave the bank $45 billion of rescue money in two bailouts, and then agreed to convert the preferred shares it bought from the bank into common stock.

But since that conversion, the bank's shares have rallied some 40 percent, and the government could be sitting on billions of dollars of profits.

The difficulty will be in selling a large block of shares without causing the bank's share price to crater, cutting in the government's profit.

(Reporting by Dan Wilchins; Editing by Bernard Orr, Gary Hill)