At a board meeting on Sunday in New York, AIG's directors worked to hammer out terms of 79-year-old Greenberg's retirement as chief executive, the Journal said, citing people familiar with the matter. In one proposal, Greenberg would stay on as chairman, the paper said.
The board is close to selecting British-born co-chief operating officer Martin Sullivan as the next CEO, the paper said, with AIG's board is expected to vote on the matter Monday night.
AIG did not answer calls for comment.
On Thursday AIG, the world's largest insurer by market value, postponed meetings between Greenberg and two investment banks, without providing further detail, stoking talk that change may be imminent at AIG.
AIG has suffered a number of legal setbacks recently including a settlement over charges that it helped companies hide losses and guilty pleas from former executives to charges stemming from New York Attorney General Eliot Spitzer's probe of the insurance industry.
The Securities and Exchange Commission and Spitzer's office are also probing an AIG deal with Berkshire Hathaway Inc.'s General Reinsurance Corp. unit, the Journal said.