Troop levels at the border, including both active-duty military and the National Guard, have at times surpassed 5,000 since President Donald Trump began deploying them there in the fall of 2018.
At the time, defense officials told the media the mission would be "months, not years."
Pentagon spokesman Major Chris Mitchell said Defense Secretary Mark Esper received the request for his review.
Congress was notified about it Thursday night, a Pentagon official said.
It wasn't immediately clear how many troops will be requested to monitor the border through the fall of 2020, or whether any of them will be active duty.