He could also instruct US Customs and Border Protection to stop any current visa holders from those countries from entering the United States.
White House spokesman Sean Spicer said on Tuesday that the State and Homeland Security departments would work on the vetting process once Trump's nominee to head the State Department, Rex Tillerson, is installed.
Other measures may include directing all agencies to finish work on a biometric identification system for non-citizens entering and exiting the United States and a crackdown on immigrants fraudulently receiving government benefits, according to the congressional aides and immigration experts.
To restrict illegal immigration, Trump has promised to build a wall on the US-Mexico border and to deport illegal migrants living inside the United States.
None of the orders to be signed Wednesday are expected to focus on those issues.
Trump is also expected to swear in his new secretary of homeland security, retired Marine General John Kelly, on Wednesday.