WASHINGTON—The former Goldman Sachs Group Inc. executive who is the top White House economic adviser told lawmakers he could support legislation breaking up the largest U.S. banks, according to people familiar with the matter, a development that bolsters congressional efforts to reinstate the Depression-era Glass-Steagall law.

The comments by Gary Cohn, director of the White House National Economic Council, came in a private meeting with lawmakers on the Senate Banking Committee Wednesday, these people said. His remarks were...