The White House assistant and director of strategic initiatives is tipped to become Trump's top economic adviser.
Larry Kudlow, a CNBC television commentator who has informally advised President Trump on economic issues, is now the top contender to head the National Economic Council, according to three people close to the president.
During his sendoff to Cohn, Trump mentioned the dispute over tariffs, saying Cohn "is not quite as strong on those tariffs as we want".
Since joining the administration in early 2017, Liddell has worked closely with Jared Kushner, the president's son-in-law and senior adviser, on efforts to streamline and update some government functions.
Trump was still hearing last-minute pleas from opponents of the tariff plan, and White House officials said they couldn't predict how the day would shake out. Mexico, Canada and Australia have been exempted from the tariffs and Trump has left open the possibility that other nations could get exemptions.
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Peter Navarro, a trade adviser to Mr Trump who promoted the tariffs, has also been touted as a candidate for the top economic job, though he has said he is not in the running. "We agree on most", Trump said.
The president has always wanted a prominent business figure to oversee the council, according to people who have spoken with him.
However, a firm decision has not been made Christopher P. Liddell, worked as the Chief Financial Officer (CFO) for Microsoft and later for General Motors.
The source cautioned however that the offer had not been extended formally to Kudlow and warned that Trump would still change his mind.