According to the people, the former MetLife CEO is frustrated with the constraints of leading a company majority-owned by the government, the paper said.
The Journal said Benmosche has complained to AIG's board about the outcome of the Treasury Department's pay review which slashed pay for a number of AIG executives by 91 percent from 2008.
AIG told CNBC it had no comment on the story.
When the credit crisis hit last year, the U.S. government rescued AIG from the brink of collapse with a loan bailout package worth up to $182.5 billion in exchange for an 80 percent stake in the insurer. It is one of seven big companies the Treasury Department ordered to cut top executives' salary and bonuses in half, starting this month.
Under the plan, cash salaries for the top 25 highest-paid executives will be limited in most cases to $500,000 and, in most cases, perks will be capped at $25,000.
For the already struggling companies, the plan has introduced concerns about so-called brain drain, as the executives targeted by "pay czar" Kenneth Feinberg rank among the most talented and productive at their companies.
Benmosche took over from Edward Liddy in August, making him AIG's third CEO in less than a year. Under a package approved by Feinberg over the summer, the AIG CEO will get compensation of about $10.5 million.
The New York-based company last week said it was profitable for the second straight quarter as its core insurance operations continue to stabilize, and reported that the amount of its government financial assistance dropped by 4 percent during the period.
Its results got a lift from the increasing value of investments it still holds that soured last year and helped drive it to the brink of collapse. But Benmosche has warned that earnings will remain choppy as the company executes its restructuring plan.
AIG is spinning off two major life insurance businesses — American International Assurance Co., or AIA, and American Life Insurance Co., also known as ALICO — as it looks to repay the government.