Speaking on condition of anonymity, the official confirmed the new ban could come into place on Wednesday.
It comes after the White House pushed back the release of the new executive order to address legal concerns.
President Trump has said the new order will tackle legal issues raised in Washington state, San Francisco and elsewhere about the original order, which was issued on January 27.
The order stopped all refugees from travelling to the US for 120 days and banned Syrian refugees indefinitely.
The travel ban sparked chaos at airports around the world with travellers held at airports and pulled off planes bound for the US.
Protests broke out across the world with federal courts temporarily blocking the order.
Thousands attended a rally outside Downing Street.
Mr Trump has criticised the courts for attempting to stop his travel ban and has vowed to overturn the temporary block.
The new order is expected to be a “more streamline version” of the January restrictions.
Last week White House advisor Stephen Miller told Fox News the new order will have “minor technical differences” but will “have the same basic policy outcome”.