NEW YORK/WASHINGTON (Reuters) - The Treasury Department plans to sell a large piece of its stake in American International Group in two stock offerings next year, officials briefed on the situation told Reuters.

It would sell any remaining stock in AIG in 2012, the sources said.

The government will own 92.1 percent of AIG after a recapitalization plan closes by the end of first quarter, and perhaps as soon as December 31.

The sale would mark a major step in getting the government out of its investment in AIG, which received a $182.3 billion bailout package during the financial crisis.

The stock sale will help the government make a profit on the bailout if the offering is roughly $30 per share or higher. The Treasury’s stake is worth about $90 billion at the current share price. It spent $49.1 billion for that stake.

AIG’s shares were up 2.4 percent at $54.69 during morning trading on the New York Stock Exchange.

The U.S. government has seen strong market appetite for stock in bailed-out companies in the past few months, allowing it to be more aggressive in winding down its stakes in companies like Citigroup and General Motors.

The AIG bailout was arguably more controversial and risky than either of those deals as the headline number was higher and the company teetered on the brink of bankruptcy and a fire-sale breakup after the last-minute rescue.

Since then, AIG, under Chief Executive Robert Benmosche, has sold several businesses, leaving property-casualty and U.S. life insurance operations at its core.

The Treasury plans to sell about one-fifth of AIG in the first offering, which is expected in the first half of 2011 and perhaps as soon as March, sources have said.

AIG and the Treasury would sell stock in that offering, which could exceed $10 billion, sources have said. That would place it among the largest secondary share offerings in history.