Liddell is now the White House's director of strategic initiatives and is said to be a key ally of Jared Kushner in an administration rife with internal feuds.
CNBC's Jim Cramer reported on Monday that Larry Kudlow, with whom Cramer hosted a show from 2002 to 2005, is the front-runner.
"Like Cohn, Kudlow is a free trade advocate, co-writing an op-ed in the National Review earlier this month saying of Trump's tariffs: "...now we are imposing sanctions on our own country, putting up tariffs supposedly to make Americans more prosperous.
Kudlow is a CNBC contributor and former Reagan administration official.
Manchester United & Jose Mourinho dumped, Sevilla and Roma progresses
Jose Mourinho has spent more on just six transfers since taking over at Manchester United than Sevilla's whole squad is worth. We got in the right positions but the last pass was not good enough and that's what killed us today.
"I'm looking at Larry Kudlow very strongly. I think we're going to go through a circular trend of a much more restrained free market", he said then.
Peter Navarro, a trade adviser to Trump who pushed for the steel and aluminum tariffs, has also been touted as a candidate for the top economic job, though he has said he is not in the running.
In a cabinet meeting on Thursday, Trump teased Cohn for not being as strong on tariffs as he would prefer. "He now has come around to believing in tariffs".
The president said last week that Cohn, the former top Goldman Sachs executive, was likely to return to his administration in the future.
A senior White House official said the president wanted to reshuffle his team with a view to launching talks with North Korea, following last week's spectacular announcement of a meeting between Trump and Kim Jong Un.