He also called for an "exit strategy" for government involvement in AIG. "Today, AIG owes taxpayers $36 billion and taxpayers own 61 percent of the company," Bachus said. "It is imperative for Treasury to map out an exit strategy from AIG's bailout in order to protect taxpayers."

While the SIGTARP report says there is currently no designated federal regulator for AIG, and adds that it remains unclear how the government will oversee AIG in the future, it does note that there are two avenues for federal regulation going forward.

The options include oversight of AIG's non-insurance units through the Fed's authority to regulate thrift-holding companies, and the possible designation of AIG as a systemically important financial institution (SIFI).

If the Financial Stability Oversight Council designates AIG as a nonbank SIFI, AIG would be subject to Federal Reserve examination, enforcement, and supervision, the report notes, adding that AIG's senior management expects and has begun preparing for such a designation.

But the report points out the challenges the government faces, stating, "Regulatory oversight of AIG will be an enormous undertaking, presenting challenges in examination, enforcement, and supervision, particularly as it relates to risk, given AIG's history."

The report also gives an update on AIG's Financial Products unit. The activities at AIGFP, including selling credit default swaps on $2.77 trillion notional amount of CDS is widely attributed as the reason the company needed government aid to stay alive.

The SIGTARP report says AIG has sharply reduced its CDS portfolio to one-tenth its former size, from about $2 trillion in net notional value in 2008 to about $168 billion in net notional value at the end of 2012's first quarter.