Departing US Treasury Secretary Timothy Geithner said Friday he would not accept an invitation to serve as the chairman of the Federal Reserve. In his last day as the head of the Treasury, Geithner, when asked about the prospect he might replace Fed Chairman Ben Bernanke, said, "Not a chance. I have great respect for the institution, but that will be someone else's privilege." Geithner, who was president of the New York Fed before taking the helm at the Treasury, has been the target of frequent speculation that he would move over to the Federal Reserve, rather than to New York, where his family has already moved to allow his son to complete high school there, the Los Angeles Times reported. Provided Bernanke leaves as expected at the end of his second term in January 2014, the door is open for Fed Vice Chair Janet Yellen to take his place. Yellen was formerly the president of the Fed's San Francisco district bank. Deputy Treasury Secretary Neal Wolin will run the Treasury until the Senate acts on President Barack Obama's nomination of outgoing White House Chief of Staff Jacob Lew to succeed Geithner. Geithner has not announced any professional plans as of yet. His plans to travel with his wife and relax with his family, the Times said.