MetLife, the largest publicly traded U.S. life insurer, may pay roughly $8 billion of the purchase price in stock and the rest in cash, according to the source.
The terms of any deal had not been finalized, though, and the mix could change, the source said.
MetLife spokesman Christopher Breslin and AIG spokesman Mark Herr declined to comment on the news that was first reported by Bloomberg. The source is anonymous because the talks are not public.
Alico, which was founded in 1921, sells life insurance and retirement products to 19 million customers in 54 countries.
A sale of Alico would be the largest for AIG since its September 2008 bailout, and a transformational deal for MetLife in the fast-growing international markets.
Last week, MetLife confirmed it was in talks to buy Alico but hadn't reached a deal.
There is no certainty MetLife will reach a deal for the AIG unit, Chief Executive Robert Henrikson said on a conference call last Wednesday, adding the insurer does not need an acquisition to meet its business objectives.
Management added on the call the company would not sell any current businesses to finance a possible deal, nor would it use capital in an off-shore reinsurance unit toward a deal.
AIG, which was propped up by a $182.3 billion U.S. aid package, has announced some two dozen deals to sell assets for more than $11.9 billion so far, as part of its efforts to pay back taxpayers.
AIG's shares were up 91 cents, or 4.1 percent, at $23.07, while MetLife was up $1.45, or 4.4 percent, at $35.11, both in afternoon trading on the New York Stock Exchange.
(Reporting by Paritosh Bansal; Editing by Leslie Gevirtz, Bernard Orr)