Trump has yet to make a decision about that post, which has sweeping authority in areas such as economic and tax policy.
The fight has spilled into public view, with advisers such as billionaire Elon Musk promoting Lutnick for the position and criticising one of the alternative candidates, Scott Bessent, as too “business as usual”.
Commerce is smaller than the treasury department, with a workforce of about 50,000 people. Beyond its role in the US-China trade and tech war, its responsibilities include patent approvals, publishing economic data, and conducting the US census.
Lutnick, a native of Long Island, New York, is a long-time Republican and supporter of Trump, with whom he overlapped in the New York social scene.
He has explained his support for the president-elect by describing himself as a “strong capitalist” and saying Trump has a “competitive growth model”.
During the campaign, he served as a spokesman for some of Trump’s most radical plans, including wide-ranging tariffs and the elimination of the income tax.