President Donald Trump believes top economic advisor Gary Cohn will resign from the White House if the administration follows through on a recently announced plan to impose tariffs on imports of steel and aluminum, according to a report from Bloomberg News citing sources.

A source familiar with Cohn, meanwhile, told CNBC that Cohn is actively contemplating his future.

A White House official told CNBC that it is likely the tariffs will be imposed, because the president has already announced it publicly. If there are any differences in the ways the tariffs apply to specific countries, the official said, it would be that the tariffs would be tough for all countries and even tougher for some.

Cohn has been working behind the scenes to stop the tariffs, or at least mitigate their effects. He has scheduled meetings between Trump and executives from U.S. metals industries to try and dissuade Trump from moving forward with his protectionist trade goals, Bloomberg News and Politico reported, both citing sources.

Trump on Thursday announced a 25 percent tariff on steel and a 10 percent tariff on aluminum. The new trade protections, Trump said at the time, would be implemented the following week.

Amid the trade policy tug of war, Trump said in a tweet Tuesday morning that the White House still has "some people that I want to change."

Trump tweet: The new Fake News narrative is that there is CHAOS in the White House. Wrong! People will always come & go, and I want strong dialogue before making a final decision. I still have some people that I want to change (always seeking perfection). There is no Chaos, only great Energy!

The White House did not immediately respond to CNBC's request for comment on Bloomberg's story about Cohn.

Tuesday, Treasury Secretary Steven Mnuchin, Cohn's fellow Goldman Sachs alum in the White House, backed the tariffs, but tried to tamp down talk of a trade war.

"We're not looking to get into trade wars. We're looking to make sure that U.S. companies can compete fairly around the world," Mnuchin told a House panel.