Belichick said on Sirius XM NFL Radio that White is a "very interesting and versatile player."
"He does a good job in the passing game and in the running game -- both inside and outside," Belichick said. "Blitz pickup -- we have a pretty extensive offense for him to learn, but he’s working hard at it.
"We’ll just let him go and see how it goes, but I think he has the ability to compete on all three downs, in both the running game and the passing game."
Brady said White hasn't seemed like a rookie early on.
The Patriots selected White in the fourth round of the 2014 NFL draft out of Wisconsin.
White rushed for 4,015 yards and 45 touchdowns in four seasons for the Badgers, including 1,000-yard seasons in 2010 and 2013.
- Ben Estes