Cobble was a two-year starer for the Wildcats. The 6-foot, 338-pound Louisville native recorded 84 tackles during his career, including seven tackles for loss and three quarterback sacks.
Rumph had his best season as a Cat in 2013, recording 47 tackles, six tackles for loss and two sacks. The 6-3, 320-pound South Carolina native was a second-team All-SEC pick by Athlon Sports.
He was a three-year starter at UK, recording 126 tackles, 15 tackles for loss, seven sacks and two forced fumbles.
If Rumph makes the Falcons' roster, he would join another former UK defensive lineman, Corey Peters, on the team.
Kentucky has had 48 players sign NFL contracts over the last seven years.