Treasury Secretary Steven Mnuchin said Thursday the removal of the tax deduction for state and local taxes remains an important part of the administration's reform plan.

"We can't have the federal government continue to subsidize the states," Mnuchin told CNBC's "Squawk Box" in a live interview. "That's a major loophole that we're trying to close in simplifying taxes."

He spoke as the administration is trying to usher its tax reform plan through Congress.

The main tenets of the proposal are a sharp reduction in corporate taxes, as well as a reduction in the number of brackets and a break for middle-income filers. Opponents say benefits will fall too much for the wealthiest, however, and even some congressional Republicans object that the plan will blow up the budget deficit.

While providing upwards of $1 trillion in tax relief, the White House plan seeks to pay for it through economic growth and the elimination of certain deductions.

Among the most controversial has been the one for state and local taxes, often referred to as the SALT deduction. High-tax states like New York, New Jersey and Connecticut would get hit especially hard. Reports have indicated that President Donald Trump is unhappy with removing the SALT deductions as it would penalize middle-class earners.

"That's one of the issues that people talk about. I understand the issue very well," Mnuchin said. "I've lived in New York and California."

However, he would not commit to keeping the SALT deductions.

One area he did say the administration is steadfast on is the 20 percent corporate tax rate. The U.S. levy is the highest in the world at 35 percent, and Mnuchin said that while there's room for talk on other issues, the corporate rate is not one of them.

"The president made it clear that he wants 20 percent. That's the one part of this bill that's not negotiable," Mnuchin said.

On other tax issues, he said the administration also is committed to removing the estate tax and the alternative minimum tax, both of which also are aimed at higher-income filers.

In addition to tax reform, Mnuchin has been reported to be pushing Trump to name Federal Reserve Governor Jerome "Jay" Powell as the next central bank chair. Powell and former Fed Governor Kevin Warsh are believed to be the front-runners to replace Janet Yellen when her term expires in February.

However, Mnuchin deflected questions about the issue. He said Trump remains committed to naming who will be the next chair soon, though there is no exact timetable. Trump has indicated he will reveal his next Fed chair in coming weeks.