GE Capital has petitioned the US regulator to remove it from the list of financial institutions that are deemed too big to fail following a judge ruling in MetLife's favour yesterday.
GE claims that reducing its balance sheet by half and scaling back its links to other firms mean it should no longer qualify for the tag that intensifies regulatory scrutiny from the Federal Reserve.
Chief executive of GE Capital Keith Sherin said:
Our submission details the complete transformation of GE Capital. Our plan to change our business model, shrink the company and reduce our risk profile has been successful.
Meanwhile AIG could also apply for an exemption from the regulation, chief executive Peter Hancock said in an interview with CNBC.
Though Hancock said AIG was "reserving judgment" for now, adding "the whole world was somewhat surprised [by the MetLife ruling]."
AIG was forced to take a $182bn (£126bn) bailout from the US government in 2008 and was one of the main causes of companies other than banks being tagged as too big to fail.
GE Capital has been attempting to shake off the brand since April last year, halving its assets to $265bn (£184bn) from $549bn at the end of 2012.
GE Capital claims to have stopped lending to consumers in the US and cut down its real estate debt by 75 per cent to focus on its core business of technology and manufacturing.
It has also ended its real estate equity and reduced outstanding commercial paper by almost 90 per cent.
The financing arm of General Electric was added to the list of systemically important financial institutions (SIFIs) by the Financial Stability Oversight Council (FSOC) in 2013.
Yesterday shares in US insurance giant MetLife surged after a judge overturned the government's decision that the company is a systemically important financial institution (SIFI).
Shares closed up by five per cent in New York. MetLife has been lobbying against the legislation for a year, though it could now be appealed by the government.