"I don't have any comments on that stuff," said Kudlow, a Trump confidant who also served in the Reagan administration. "I just don't want to walk through all those scenarios."
Cohn announced his resignation as director of the National Economic Council late Tuesday after clashing with protectionist forces within the administration over imposing trade tariffs.
Ever since Trump unveiled his tariff plan last Thursday, Kudlow, a former Wall Street economist, has said repeatedly that he urged Cohn to stay.
Kudlow's name has been bandied about as a possible candidate to replace the departing Cohn. But like Cohn, Kudlow has said he's no fan of the president's plan to impose broad import tariffs of 25 percent on steel and 10 percent on aluminum.
"I don't like blanket tariffs," Kudlow told CNBC, where he is a senior contributor.
Kudlow said sometimes "targeted tariffs" can work in getting the true culprit's attention. "I would have started with China," he argued. "Go after China. Canada is not our enemy."
Wall Street wants to know whether Canada and Mexico would be exempted from the tariffs. Negotiators for those two nations and the United States are currently trying to overhaul the 1994 North American Free Trade Agreement.
While there's been no confirmation from the White House on whether such exemptions are in the works, Trump signaled an openness to them if a new NAFTA deal can be reached.