American media outlets reported citing unnamed sources that Fischer is President Barack Obama’s top choice for the post.
The Wall Street Journal said the nomination is likely to come soon.
Fischer, who led the Bank of Israel in 2005-2013, would replace Janet Yellen as the second highest Fed official.
Yellen is set to take the top spot from current boss Ben Bernanke whose term ends in January.
The Senate is expected to vote on confirmation of Yellen's nomination next week, Senate aides said.
Fischer, who is a professor at Massachusetts Institute of Technology, holds US and Israeli citizenship. He resigned as governor of the Bank of Israel on June 30.
Fischer held the number two spot at the International Monetary Fund, holding that post from 1994 to 2001.
The 70-year-old was chief economist at the Washington-based World Bank from 1988 to 1990.