"I think the important thought here is he may be moving quickly towards these bilateral discussions instead of as a whole," Kudlow said.
The Canadian dollar and Mexican peso fell on Tuesday vs. the U.S. dollar in the wake of the comments from Kudlow.
A Canadian government official pointed out this was not the first time the Trump administration has suggested a bilateral, rather than multilateral, approach. The White House and Mexican government did not immediately respond to CNBC emails for comment. Canada and Mexico are the second and third-largest trading partners of the U.S., respectively.
On Friday, Trump said he "wouldn't mind" separate negotiations with the two countries. A day earlier, his administration said it would impose tariffs on steel and aluminum imports from Canada, Mexico and the EU.
In reaction, Canada last week proposed tariffs on a range of goods, including ball-point pens, toilet paper and maple sugar.
Mexico said Tuesday it will impose tariffs of 15 to 25 percent on U.S. steel products, a 20 percent tariff on U.S. pork legs and shoulders, apples and potatoes and 20 to 25 percent duties on types of cheese and bourbon.
"Canada's a different country than Mexico. They have different problems," Kudlow said. "Often times when you have to compromise with a whole bunch of countries you get the worst of the deals."
— Reuters contributed to this report.