American International Group Inc
A deal could be announced soon, the source said, though it had not been finalized and things could still fall apart. If the transaction does go through, it would be the largest for AIG since its rescue by the U.S. government in September.
AIG and Zurich declined to comment.
Zurich, Europe's fourth-largest insurer, has said it was on the lookout for deals that will bolster its North American personal lines and global life insurance businesses.
DZ Bank analyst Werner Eisenmann noted that speculation had previously centered on a purchase price of $2 billion for the AIG unit.
We therefore see a possibility of the acquisition being made. The transaction would make Zurich the market leader in the automobile market in California.
U.S. taxpayers have taken a roughly 80 percent stake in AIG, once the world's largest insurer, in exchange for providing up to $180 billion in financial support.
The company is trying to ditch assets in a bid to pay back the government, but has struggled to find buyers for big-ticket items.
DZ Bank's Eisenmann said Zurich has intensive knowledge of the auto market, although any capital increase needed for the deal would be a negative factor.
Shares in the company were up 1.1 percent at 194.3 Swiss francs at 0856 GMT, in line with gains by the DJ Stoxx European insurance index <.SXIP>.
NO PRESSURE TO OVERPAY
The auto insurance business is part of AIG's U.S. personal lines unit, which also includes selling products to high net-worth individuals through its AIG Private Client division. AIG Chief Executive Edward Liddy has previously said that the private client division is not being sold.
Fabrizio Croce, Kepler Capital Markets analyst, said Zurich should not conclude the deal before a new chief executive replaces Jim Shiro, due to step down at the end of the year.
It is no longer the task of an exiting CEO to make big acquisitions but rather to hand over the company in the most solid way, he wrote in a client note.
He added that Zurich should be careful not to overpay for the business, especially as AIG is squeezed as it has no choice ... and all its assets should therefore deflate further.
Last week CEO Liddy said AIG had reached agreements to sell 10 businesses, despite the most challenging market environment in memory.
These include the sale of HSB Group to German reinsurer Munich Re
But AIG has no intention of selling its 9.9 percent stake in PICC Property & Casualty <2328.HK>, China's top non-life insurer said on Thursday.
(Additional reporting by Emma Thomasson in Zurich, Editing by Ian Geoghegan, John Stonestreet)
(For more M&A news and our DealZone blog, go to http://www.reuters.com/deals)