Mattis is responding to a request from President Donald Trump, who says he's "bringing out the military" to address what he's calling a national emergency at the border.
The U.S. official was not authorized to speak publicly because the details had not yet been finalized and spoke on condition of anonymity.
The additional troops are to provide what one official described as logistical support to the Border Patrol. This would include a variety of things such as vehicles, tents and equipment.
There already are about 2,000 National Guard troops assisting at the border under a previous Pentagon arrangement.
Eyewitness News first reported the move on Monday during an exclusive interview with President Donald Trump.