Mitchell could be a replacement for veteran defensive tackle Jonathan Babineaux, a 12-year veteran, who set to become an unrestricted free agent.
The Falcons signed former Dolphin defensive end/tackle Derrick Shelby in free agency last season.
Mitchell was originally drafted by the Houston Texans in the third-round of the 2010 draft out of Arizona.
He started five games last season for the Dolphins was set to make $4 million in 2017. He suffered a leg injury in the opener against Seattle and was placed on injured reserve until November by the Dolphins last season.
Mitchell is also reportedly set to visit the Broncos, 49ers and Seahawks.