The insurance giant's directors have discussed plans for the business for "a while" but have not made a final decision, according to the report. The unit, which sells coverage protecting mortgage lenders and investors, accounted for only about 5 percent of AIG's pretax profit in the second quarter.
AIG has recently received pressure from key shareholders such as Carl Icahn and John Paulson to break up the company and reduce regulatory risks. Icahn, an activist investor, said this week he took a "large stake" in AIG, calling the company "too big to succeed."
AIG reports quarterly earnings Monday. Shares rose more than 1 percent in extended trading Thursday.
AIG declined to comment to CNBC.