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But the board does not plan to take any action with respect to Benmosche when it meets next Tuesday, the source said.
The Wall Street Journal has reported that the recently installed CEO had threatened to quit earlier in November, partly because he does not have discretion over pay packages for top executives.
But Benmosche said in a letter to employees last week that he was totally committed to seeing the company through its difficulties.
Benmosche said he was particularly concerned with the pay of the company's top 100 executives, which is under the purview of Kenneth Feinberg, the U.S. government's pay czar.
AIG, which has received up to $180 billion of federal aid, including more than $80 billion in loans, is around 80 percent-owned by U.S. taxpayers.
Benmosche has been frustrated with the extent of governmental oversight of the bailed out insurer, and would rather focus on improving its operations, the source said.
The company posted its second straight quarterly profit on November 6, helped by a recovery in the value of its investments.
AIG declined to comment. The source did not want to be identified because the upcoming meeting is not public.
AIG's shares closed down 50 cents, or 1.4 percent, at $35.66 on the New York Stock Exchange on Thursday.
(Reporting by Paritosh Bansal and Lilla Zuill; Editing by Phil Berlowitz)