"The timeline that we're on is that by September 3 — when Dr. Romer leaves her post — is to have that position filled," deputy White House press secretary Bill Burton told reporters Monday. "She'll obviously have a big say in who gets that position."
Burton said an announcement isn't expected this week and that President Obama is vetting candidates for the position.
Romer last week announced she would be leaving her post to return to her position as an economics professor at the University of California at Berkeley.
Vicki Needham contributed to this story.
--This story was updated a 4:50 p.m.