It is believed his frustrations relate to the difficult task of retaining talented staff at the company while also complying with pay regulations.
At a board meeting last week, Mr Benmosche told AIG directors that he was "done" with the job following a meeting with government pay czar Kenneth Feinberg, the Wall Street Journal reported.
But board members managed to persuade him to think over his intentions to resign.
This is apparently not the first time he has threatened to quit.
In August, he reportedly threatened to walk out if his $10.5 million pay package for doing the job was not approved.
AIG has received around $90 billion in bailout funds since the financial crisis began.
Earlier this month, AIG reported net profits of $455 million for the third quarter of 2009.
By Claire Archer