The appointment of Subramanian, a senior fellow at the Peterson Institute for International Economics, was recommended by finance minister Arun Jaitley. Cabinet-level approval is expected to follow.
"He is likely to be appointed soon," one of the sources said.
Modi stormed to a general election victory in May with a pledge to lift the economy out of its worst slowdown in a quarter of a century and put to work the one million young people who enter the workforce each month.
The nationalist leader has abolished a Soviet-style Planning Commission, but made an otherwise slow start on economic reforms, disappointing some supporters who had hoped that he would take decisive action to promote a recovery.