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Dodd-Frank stipulates that all banks with more than $50 billion in total assets would automatically be deemed "systemically significant," but the FSOC has broader authority to identify non-bank financial firms that could pose a risk to the system.

Under rules finalized in April, the FSOC decides which non-banks merit increased scrutiny via a three-stop process. The FSOC is preparing to enter the third and final stage of consideration for AIG, the company said, and could propose a systemically significant label soon.

The FSOC agreed in a private meeting Friday to begin notifying some non-bank financial firms that they would be entering Stage Three of their risk-assessment process. Companies have the option of appealing any designation to the regulators.

The new powers that regulators were given are meant to prevent the government from having to step in and rescue financial firms that are so integral to the economy that their collapse would threaten the entire financial system. By subjecting critical institutions to heightened protections and regulation, the government hopes to effectively bring an end to companies being "too big to fail."

Although receiving a systemically significant label would require a firm to be subject to heightened capital requirements, further stress tests and other increased regulation, some congressional Republicans have blasted the new tool as actually giving firms a competitive edge by showing that the government deems them "too big to fail."

Financial firms have largely resisted the label, however, and are wary of the increased requirements and oversight that it brings.

The potential labeling of AIG comes even as the insurance company is still working to free itself from a government lifeline. In September, the Treasury Department sold $18 billion worth of shares in the company, netting a $12.4 billion profit. The government at one point was an 80 percent owner in the company, but still holds a roughly 21 percent stake in the company.