The updated order, the final version of which should be released soon, also exempts travelers who already have a visa to travel to the US.
President Trump's first executive order curtailing immigration, issued earlier this month, banned travel to the US from seven Muslim-majority countries.
But the Supreme Court temporarily suspended the move, something that riled the President.
According to a senior administration official, a revised travel ban order will target only those seven Muslim-majority countries: Iran, Iraq, Syria, Yemen, Somalia, Sudan and Libya.
The official said that green-card holders and dual citizens of the US and any of those countries are exempt from the proposed new ban.
The new draft also no longer directs authorities to single out Syrian refugees when processing new visa applications, according to the source.
While the draft order is still subject to change, it could be signed off as early as this week.
Asked about the revised order, White House spokeswoman Sarah Huckabee Sanders said the document circulating was a draft and that a final version should be released soon.
Mr Trump's original executive order triggered chaos at airports around the world, as travelers were detained when the order rapidly went into effect.In its original form, the order temporarily suspended all travel to the US for citizens of those seven Muslim-majority countries for 90 days.
The original order also called for Homeland Security and State department officials, along with the director of national intelligence, to review what information the government needed to fully vet would-be visitors and come up with a list of countries that can't or won't make the information available.