Amy Brundage, an Obama spokeswoman, tweeted that the president "has not yet made a decision."
"The latest rumors this morning in the Japanese press aren't true," she said.
The finalists for the job appear to be Summers and Janet Yellen, currently the Fed's vice chairwoman, The Wall Street Journal reported. The administration is being lobbied by supporters of both candidates.
Several hundred economists signed a letter this week backing Yellen, USA Today said.