"They've indicated that they are working to get us a nominee in time for us to do our due diligence," the aide said.
White House spokeswoman Amy Brundage said the Obama administration's media team would not comment on a personnel matter "until the president has made his decision and is ready to announce them."
While indications are that Bernanke will leave the Fed when his term ends on Jan. 31, 2014, the short list for the next Fed chairman includes Bernanke himself, The New York Times reported Friday.
Bernanke could be persuaded to stay, although President Obama said in an interview recently the chairman, in his second four-year term, "already stayed a lot longer than he wanted or was supposed to."
People familiar with the matter said Treasury Secretary Jack Lew was putting together a short list of possible replacements.
The candidate most frequently mentioned as the front-runner is the current vice chairwoman, Janet Yellen, the Times said.
Yellen served as the chairwoman of the Council of Economic Advisers during the Clinton administration. She has also been president of the San Francisco Federal Reserve and a Fed governor.
Other strong possibilities for the position include former Treasury Secretary Timothy Geithner, who has said he does not want it, former Vice Chairmen Alan Blinder, now a Princeton University professor, and Christina Romer, who previously headed the White House Council of Economic Advisers.
Former Treasury Secretary Lawrence Summers could also be considered a candidate for the post, the Times said.