American International Group
The insurer may pay any penalties and future legal fees in Greenberg's case with New York Attorney General Andrew Cuomo, the newspaper said, adding that the agreement is not certain.
A deal could also include the resolution of a $1 billion claim AIG has against Greenberg and another former AIG executive in a civil lawsuit, the WSJ reported.
AIG may also reimburse Greenberg, who has agreed in recent years to pay millions of dollars to settle other cases related to his time at AIG, some of these costs as well as those of any future settlements, according to the newspaper.
A spokeswoman for AIG declined comment and a spokeswoman for Greenberg's lawyer did not immediately return calls.
Greenberg and AIG said in August they agreed to privately arbitrate the shareholder lawsuit in a bid to bring an end to an extended legal fight.
AIG's total bailout package from the government, which includes the purchase of toxic assets, is as much as $182.5 billion. The insurer, which has not drawn all the funds available, currently owes about $80 billion in loans.
(Reporting by Elinor Comlay, editing by Leslie Gevirtz)