Daniel Tarullo, a Georgetown University law professor who has advised Obama on trade issues, is thought by many Washington lobbyists to be to a top candidate for the job.
Tarullo worked for former President Bill Clinton in the 1990s -- first as an assistant secretary of state for economic and business affairs and later as a White House adviser.
Other possible candidates include Mike Wessel, a longtime aide to former House Democratic Leader Richard Gephardt and current member of U.S.-China Economic and Security Review Commission, a congressional watchdog group.
Lael Brainard, an international economics adviser in the Clinton White House now at the Brookings Institution, spoke for the Obama campaign at a debate on trade policy, prompting speculation she could be in line for an administration job.
Several argue Obama should tap a politician like former Rep. Cal Dooley, a California Democrat, since working with Congress would be a big part of the job.
However, Dooley's support for Bush administration trade deals makes him an unpopular choice with labor groups.
Some business lobbyists want Obama to consider veteran U.S. trade negotiators Peter Allgeier and Rufus Yerxa for the post.
Allgeier is the current U.S. ambassador to the World Trade Organization in Geneva. Yerxa was a deputy U.S. trade representative in the Clinton administration and has been a deputy director general of the WTO since 2002.
"Either one of those would be fantastic choices, as would some of the other names bandied about," said Doug Goudie, director of international trade policy for National Association of Manufacturers.
That includes Stuart Eizenstat, who held the job of deputy Treasury secretary and other senior economic posts in the Clinton administration, Goudie said.
We may not know for a while, though: "typically the job of U.S. trade representative is often one of the last to be filled."