Syrian refugees were banned under the president's initial immigration order, which has failed to overcome legal challenges.
The new draft contains an exemption for green card holders and citizens from the seven countries who are also U.S. citizens, one of the officials said — a difference from the order signed last month.
Another senior administration official said Trump is expected to sign the order "by the end of the week."
Trump has expressed frustration in person and on social media over his stalled travel ban, often targeting the courts and the judges who have ruled against provisions of the order.
He and his administration have argued repeatedly that the first order falls within the president's authority to ban any class of aliens deemed a potential threat to the security of the United States. But the federal judges unanimously ruled to uphold a restraining order delaying the ban, which the administration elected not to pursue in that form.
In their ruling, the judges said Trump's previous remarks about a Muslim ban could be used as evidence and that the government did not present evidence that nationals from the affected countries perpetrated attacks in the United States.
The rocky rollout of the first executive order resulted in extended detentions of immigrants at airports and sparked protests around the country, though Trump and other White House officials repeatedly called the rollout a success.
As of Monday afternoon, the revised order was still considered to be in an early drafting stage, according to the administration officials.