Gunnell, who transferred from Arizona to Memphis in December 2020, missed all of the 2021 season because of a leg injury. He reentered the transfer portal last month after participating in the Tigers' spring game.
Gunnell, who was Arizona's starter in 2020 and played eight games there in 2019, has three years of eligibility remaining.
Gunnell started the Wildcats' first three games in 2020 before suffering a shoulder injury in a loss to UCLA. He passed for 625 yards and six touchdowns with two interceptions. The 6-foot-6, 225-pound Gunnell split time with Khalil Tate in 2019, starting three games and finishing with 1,239 passing yards and nine touchdowns with an interception.
A four-star recruit from The Woodlands, Texas, Gunnell was rated as ESPN's No. 15 pocket passer in the 2019 class.