Treasury will seek to sell off a big chunk of its holdings in AIG (AIG), the government-owned insurance company, in the first quarter of 2011, Reuters reports.

Hours later, AIG, Treasury and the Federal Reserve signed off on a deal formalizing the terms of the latest restructuring of AIG’s relationship with its government rescuers, pointing to a likely government stock sale in 2011.

Under the deal outlined Wednesday, AIG will repay the Fed with funds it borrows from Treasury and will then swap those loans for common shares, giving Treasury 92% of the company. AIG will have the right to sell as much as $7 billion* in shares to raise money for itself between now and August; after that, Treasury can ask it twice a year to hold offerings under which the feds can sell down some of their holdings.

Those terms point to coming sales of the government’s AIG stock, though the details seem to differ from the Reuters report earlier.

Citing sources familiar with the matter, Reuters said the feds could be looking at a stock sale in the range of $10 billion. That could knock taxpayers’ stake in New York-based AIG down into the low 70% range.

Treasury said it’s early yet to talk about a stock sale, but it’s easy to see where the government would be feeling good about its ability to cash out some of its investments in bailed-out companies.

Take this week’s $10 billion sale of the last of Treasury’s Citi (C) stake. In that case, the government was able to score a $12 billion profit on a $45 billion commitment to prop up the third-biggest U.S. bank.

Perhaps more impressive, Treasury was able to unload more than a quarter of Citi’s stock on the market over a year without hurting the market price. Treasury said it’s early yet to put AIG in the same breath as Citi and GM (GM), which the government sold a big stake in last month, but there is no mystery the feds would like to, say, monetize AIG as soon as possible.

We are completely focused on finishing work on the plan to restructure AIG and put it in a stronger position to begin repaying taxpayers and return fully to the private sector.   We are making good progress on the recapitalization plan but it is premature to speculate about next steps.

It will likely be a longer road for the government to get out of AIG alive. At one point various arms of the government were into AIG to the tune of $182 billion in commitments, though much of that has been repaid or restructured.  

A deal announced in September took the remaining Federal Reserve loans to AIG, converted them into common shares and gave them to Treasury so the department could repeat its success in the Citi deal. AIG nodded to that deal in its statement Wednesday.

We hope to be able to go to the market with a public offering of AIG this spring, but we have work to do to make that happen. We are working as diligently as we can to achieve this as quickly as possible, subject to market conditions. We remain committed to executing the steps and meeting all conditions in the recapitalization agreement as soon as possible.

Matching the success of the Citi sale won’t be easy, but investors’ sudden fear of bonds could help. The yields on government bonds around the world have surged in recent days in what may be a sign that investors are coming to grips with the scale of the financing problems confronting all the developed economies.

A flow of investor funds out of bonds will make the business of funding all those deficits a little trickier and potentially a lot more costly. But it could create new demand for stocks – which will come in handy when it comes time to start soaking up all that AIG stock.

*Update: Originally I wrote $4 billion, but the terms are that AIG can sell $3 billion worth no matter what and an added $4 billion if Treasury says so. I apologize for the error.