At a board meeting last Friday, Mr. Benmosche said he wanted Mr. Golub to leave or he himself would quit, the people said. The resignation threat came after the board of the government-controlled insurer several weeks ago voted down the sale of a major overseas life insurer, AIA Group Ltd., that Mr. Benmosche supported.
Separately, AIG is considering a sale of two Japanese life-insurance companies for roughly $5 billion, people familiar with the matter said.
An AIG spokeswoman declined to comment.
Mr. Benmosche, who took the helm of AIG last August, has previously threatened to leave. His latest stance appeared an effort to signal he needs authority to make decisions for AIG and determine the fate of major assets, said people familiar with the matter.
Questions about his influence arose over Memorial Day weekend, when Mr. Benmosche pushed for a sale of AIA to the U.K.'s Prudential PLC at a price lower than a $35.5 billion tag AIG and Prudential had agreed upon earlier this year. When Prudential's shareholders balked at that deal, the British insurer proposed a lower price of $30.4 billion. Mr. Benmosche backed the revision as a still-good deal for AIG that would help the company repay a chunk of taxpayer money.
But other members of AIG's board worried that the new deal wouldn't stick with Prudential's shareholders, and that an unconsummated deal at a lower price would hurt other efforts to sell the unit. Some company advisers indicated AIA could be valued at $32 billion to $36 billion following an IPO.
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Messrs. Benmosche and Golub now agree that AIG should work toward an initial public offering for AIA, which is currently the most viable and promising option on the table, one person familiar with the matter said. The aim is for an IPO of the unit to occur in Hong Kong by year end.
AIG has to sell assets in order to repay the Federal Reserve Bank of New York more than $50 billion.
A plan to sell the two Japanese life-insurance companies would represent a reversal of AIG's decision last fall to hold on to the two subsidiaries, AIG Star Life Insurance Co. and AIG Edison Life Insurance Co.
The units had been on the block but failed to fetch attractive prices as potential buyers ran into financing difficulties.
After Mr. Benmosche visited the units in Japan in October 2009, AIG said it planned to retain the companies "for the foreseeable future" in part to help stabilize their businesses.
Since then, the performance of AIG Star and Edison, along with the deal-financing environment, have improved, people familiar with the matter say. Continued interest from potential buyers also may have prompted AIG to revisit the idea of selling the two units. There is no formal sale process in place yet, people familiar with the matter said.
Analysts have long considered Prudential Financial Inc., the big insurer based in Newark, N.J., to be a logical buyer of the two companies.
Prudential Financial, unrelated to Prudential PLC, has operated in Japan for more than 25 years, and has made at least two acquisitions of Japanese insurers in that time. It has publicly stated its interest in expanding in the country.
In a report last week, Bank of America Merrill Lynch analyst Edward Spehar said Prudential Financial has the capital capacity to do deals topping $6 billion without selling more shares.
Angelo Graci, managing director at Chapedaine Credit Partners in New York, estimates AIG's Star and Edison could be worth $4 billion to $6 billion in a sale, based on their book values.
Prudential declined to comment on any possible acquisition activity related to the AIG properties.