Sources from the business community told The Hill they are hearing that the nomination is in the works.
Krueger has reportedly decided to head back to teach at Princeton University in September, where he has tenure.
Furman spent some time in front of the cameras in February warning about the effects of the $80 billion sequester budget cuts on economic growth ahead of their March 1 implementation. He said the effects would get worse over time if the across-the-board spending cuts were left in place.
Furman would need to go through the Senate confirmation process to the Cabinet spot.
Krueger, whose job is keeping Obama abreast of economic data, is the White House's face of the closely watched monthly jobs report.
The CEA chairmen have a habit of returning to the academic world.
Christina Romer returned to the University of California at Berkeley in 2010 and Austan Goolsbee went back to the University of Chicago in 2011.
Erik Wasson contributed.
This story was updated at 2 p.m.