According to Fox News, the CEO is thought to be one of many top representatives from the financial institution to have recently been engaged in recent meetings over the failure with the regulator.
Questions are believed to have surrounded the use of Repo 105, a banking practice which can be used to provide an artificial impression of the health of an institutionâs balance sheet.
Other lines of enquiry are focusing on whether senior figures misled the markets about Lehman Brothersâ stability during the period leading up to its collapse in September 2008.
Joseph Gregory, former president and Erin Callan, ex-chief financial officer, are both reported to be among the executives who could be facing charges alongside Mr Fuld.
An SEC spokesman told City AM: âWe cannot confirm or deny any ongoing investigations.â
Lehman Brothers filed for bankruptcy on September 15th 2008 at the height of the global credit crisis.
By Jim Ottewill