Citigroup Inc. on Thursday said it may conduct a reverse stock split as part of an exchange offer that could give the U.S. government a 36 percent stake in the bank.

As part of a Feb. 27 government bailout, the third-largest U.S. bank is seeking to swap $27.5 billion of preferred securities for common stock, with the government converting up to $25 billion of its preferred securities for common stock.

Citigroup said it will also seek shareholder approval to conduct a reverse stock split. It proposed seven possible exchange ratios, ranging from 1-for-2 to 1-for-30, and said the split could take place before June 30, 2010.

A reverse split reduces a company’s shares outstanding and is often used to boost a very low share price. It does not change the value of an investor’s holdings.

Citigroup has 5.5 billion shares outstanding and has said the preferred stock exchange offer could increase that number to 21 billion, prior to the effect of any reverse split.

Shares of Citigroup closed Wednesday at $3.08. They rose to $3.10 in premarket trading.