It would sell any remaining stock in AIG in 2012, the sources said.
The government will own 92.1 per cent of AIG after a recapitalisation 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 $182.3bn (£117.4bn) bailout package during the financial crisis.
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 said.
AIG and the Treasury would sell stock in that offering, which could exceed $10bn, sources have said, placing it among the largest secondary share offerings in history.
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 $90bn at the current share price. It spent $49.1bn for that stake.
AIG's shares were up 2.4 per cent at $54.69 during morning trading on the New York Stock Exchange.
The US 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 US life insurance operations at its core.