President Donald Trump is expected to formalize the details of his tariff proposal, including any carve outs or exemptions, on Thursday or Friday.

White House press secretary Sarah Huckabee Sanders said at a news briefing Wednesday that she expects Trump to sign off on the measures this week.

"We expect that the president will sign something by the end of the week, and there are potential carve-outs for Mexico and Canada based on national security, and possibly other countries as well," Sanders said.

At the same time, White House officials told CNBC, there could be a conversation this week around additional trade actions the White House is considering.

Officials said there is a basket of trade-related ideas under consideration, but it is not clear what ideas will ultimately be embraced by the president.

When asked whether there will be carve-outs for Mexico, Canada or NATO allies, Sanders told the briefing, "It'll be country-by-country and based on national security."

Trump's shock decision last week to impose 25 percent tariffs on steel imports and 10 percent tariffs on aluminum demonstrated that he was putting into practice the protectionist policies he pushed during his election campaign. The announcement set off a wave of uncertainty in markets.

Investors found further reason for concern with Tuesday's resignation of top White House economic advisor Gary Cohn, a Wall Street veteran who was opposed to the tariffs. Stocks declined Wednesday as traders absorbed the development.

Trump, in recent tweets, has hinted at other potential trade actions and areas of interest. On Wednesday, he singled out China and mentioned intellectual property theft in a pair of tweets.

TRUMP CHINA TWEET

TRUMP IP THEFT

On Saturday, Trump threatened to slap tariffs on European cars.

TRUMP CAR TWEET

The White House is planning a late afternoon signing event, a source familiar with the matter told CNBC. Reuters, also citing a source, said it would take place at 3:30 pm ET on Thursday.

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CNBC's Kayla Tausche contributed to this report.