Bernanke, a governor of the U.S. Federal Reserve system, had not formally been offered the position but had held meetings with key economic staff, the Financial Times reported Friday.
James Poterba, a professor at the Massachusetts Institute of Technology was also sounded out but made it clear he was not interested in the job.
Bernanke has the support of other economists and policymakers in and close to the administration and would, the FT said, accept the post if it were offered. He is also seen as a supporter of the broad outline of the Bush administration's aims of reforming Social Security, including introducing personal accounts, and tax reform.
"The administration has a problem with economic heavyweights," said David Hale, a Chicago economist. "Mankiw is a very smart guy but got into trouble for his comments on outsourcing. Bernanke could end up being the heavyweight the administration has not had in recent years," Hale said.
Mankiw is expected to return to academia once he leaves the CEA.