The source requested not to be named, the Times said.
Krueger is a tenured professor at Princeton University and is expected to return to his position there. Furman is currently the deputy director of the council, which advises the president on economic matters.
Furman is one of the original members of President Obama's economic advisement team, the Times said.
He has a doctorate in economics which he earned at Harvard University. He has worked on the Hamilton Project, which is a research unit associated with the Brookings Institute.