American International Group Chairman Steve Miller said on Thursday the bailed-out insurance giant may eventually want to buy a life insurer outside the United States, including possibly a larger stake in the spun-off subsidiary AIA Group <1299.HK>, as confidence in its turnaround grows.

Miller, in an interview on the sidelines of the World Economic Forum in Davos, Switzerland, said any decision was probably two to three years down the road, but as the company thought about its possible alternatives in the future, rebuilding a global life insurance business was a logical issue to consider.

Miller's comments are a remarkable reversal for AIG, which was bailed out by the U.S. government at the height of the financial crisis in 2008 and is still majority owned by taxpayers. The thinking at AIG since the crisis had largely been focused on divesting assets and paying back the government.

While that continues to be the singular focus of the company, Miller said the board has been thinking of longer-term strategy as well.

If you look at the company, you are a global (property and casualty) company and a domestic life company, which begs the question, 'What about the fourth box on the chart?' Do you want to be global in life or you want to not be in life? Those are all valid strategic questions. And one way or the other we will probably rebuild an international presence in life, Miller said.

It's an obvious strategic question. It is very premature to be speculating about it right now.

The question of what to do with AIA is an important one for AIG because of the outsized impact it has on the company's financial results every quarter, and because AIA could give the company back the international profile it once had.

AIG spun off two-thirds of AIA in a blockbuster Hong Kong IPO in the fall of 2010. The sale was seen as a crucial milestone in AIG's efforts to reorganize and remain a going concern while also repaying its $182 billion bailout.

But the remaining one-third stake has caused wild swings in AIG's quarterly results since, leaving the company hostage to the vagaries of the Hong Kong stock market. Miller said that was untenable.

TWO POSSIBLE OUTCOMES

I don't see us holding a third of the company forever, Miller said. One of two things is going to happen -- either we will monetize that one-third interest in AIA and use it for some other corporate purpose, or in fact if the stars were aligned in a different way, possibly we would want to re-acquire a portion of it.

AIG's one-third stake in the company is housed inside a special purpose vehicle. The U.S. Treasury owns a preferred interest in that vehicle, and the assumption had long been that AIG would ultimately sell its remaining AIA interests to pay off that Treasury position.

But Chief Executive Bob Benmosche surprised investors last year when he said that AIG might like to keep the AIA stake, and instead find the proceeds to pay off the Treasury elsewhere.

Benmosche's interest is understandable, as AIA is still a huge contributor to AIG in good times. In the second quarter of 2011, with AIA shares rising, AIG booked a gain on the investment of $1.5 billion, making up almost all of the company's net profit for the period.

But with the stock falling alongside global markets in the third quarter, AIG booked a $2.3 billion loss on that stake.

Smoothing out such uncertainty may be attractive to AIG, particularly as it ramps up efforts to reintroduce its brand name in the market. Last week it said sales skyrocketed at a life insurance subsidiary that tested switching back to the AIG brand, and this week it merged a number of employee benefits operations into one business with the AIG brand name.

Taking back AIA would also solve another problem for AIG -- it is a dominant global player in the property insurance market, but in life insurance it is more or less restricted to the United States, via its SunAmerica business.

Miller said AIG was proud of that business but was equally quick to point out it was not a global operation.

So the question that looms there is should we take the skillset that we've got in life and retirement services and go back to being what AIG used to be, which is a global life player, and the avenues to get there might be through AIA or might not, Miller said.

(Reporting By Paritosh Bansal, Writing by Ben Berkowitz in Boston, editing by Dave Zimmerman)