In response to a question about the much-buzzed about successor to Bernanke, whose second four-year term expires January 31, the official said tersely: "No decision made, no announcement imminent -- announcement likely not until the fall."
Any Obama nomination must go to the Senate, controlled by his Democratic Party, for approval. Congress returns from its summer recess after September 6.
Bernanke, who has shepherded the world's largest economy through the worst crisis since the Great Depression, has not publicly indicated he would seek a third term.
And in late June, The Wall Street Journal reported the White House was reviewing possible successors to Bernanke and was quietly assembling a short list of candidates.
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Even if he no longer helms the Fed, Bernanke likely would remain a member of the Board of Governors through January 31, 2020, when his term as a board member expires.
Bernanke, an economist and renowned expert on the Depression, was named to succeed Fed Chairman Alan Greenspan by Republican president George W. Bush.
Media speculation about Obama's choice has focused on the Fed Board's current vice chair, Janet Yellen.
But there has been recent buzz about Larry Summers, Obama's former economic adviser and a Treasury chief under the Bill Clinton administration.
Other names circulating are Timothy Geithner, who stepped down as Treasury secretary in February, and Donald Kohn, who served as vice chair of the Fed Board from 2006 to 2010.