Nearly as soon as Cohn announced his resignation on Tuesday, speculation over his replacement - and the direction of Trump's economic policy - kicked off.
"Chris has a strong interest in foreign affairs, and is a member of the Council on Foreign Relations, which is now focusing on the president's decisions on tariffs and industry protection", Hope said, questioning whether he might be able to "moderate the President's position on trade".
CNBC anchor Larry Kudlow is seen on the set of his show "The Call" in 2009.
While Kudlow has been publicly critical of the tariffs, Trump said that the longtime CNBC senior contributor has "come around" on the issue.
Other candidates for the top economic policy adviser mentioned by the media include White House director of strategic initiatives Christopher Liddell, deputy director for economic policy Shahira Knight, budget director Mick Mulvaney, and trade adviser Peter Navarro.
In a cabinet meeting on Thursday, Trump teased Cohn for not being as strong on tariffs as he would prefer.
Liddell's economic views are less clear.
Speaking to Television New Zealand in 2016, Liddell signalled a nuanced position on trade, saying he was a believer in free markets "but not unbridled free markets".