A possible Summers nomination for the Fed job has faced recent complaints—largely from liberals in the president's own party.
In a closed-door meeting with Democratic lawmakers Wednesday, Obama defended Summers. According to Democrats who were there, Obama also said he's interviewed several possible nominees, but made it clear no decision has been made.
(Read more: Obama mulls Fed pick, defends Summers)
If Obama picks Yellen as the next Fed chair, she'd be the first woman to lead the central bank. It's believed that she would continue on a Bernanke-like path concerning monetary policy.
Summers, on other hand, is viewed as someone who might shake things up a bit at the Fed, which has been engaged in extraordinary measures since the financial crisis of 2008 to help jump-start the economy.
The expected changing-of-the-guard comes as central bank policymakers try to decide when, and if, they should start to taper their $85-billion-a-month bond-buying program. Fed-watchers say a slowdown in purchases could come as soon as September.
—By CNBC's Matthew J. Belvedere. Follow him on Twitter @Matt_SquawkCNBC. Wires contributed to this report.