Altman, 64, met with Obama Tuesday to discuss the job, which involves coordinating policy-making and economic advice for the president, Bloomberg News reported without naming its sources.
Altman worked at the Treasury Department under President Bill Clinton. His appointment could be a pro-business gesture from the Obama administration, which ahs been sharply criticized by some business groups.
"The president is considering a number of qualified candidates, but he has only begun the process and no decisions have been made," White House spokeswoman Jen Psaki said.
In July, Altman wrote a column in The New York Times saying that the "poisonous dynamic" between the administration and the business community must be repaired.
"Both sides should make adjustments, but the business community -- of which I am a proud member -- especially needs to make efforts to mend this relationship," Altman wrote. "Yes, the administration has made some mistakes. But, on balance, its actions have supported business."