Hinch interviewed with the team on Thursday and his new deal could be completed as soon as Friday.
Hinch, 46, was fired by the Astros in January after he was linked to the team's sign-stealing scheme during the 2017 season. MLB suspended Hinch for the entire 2020 season before his dismissal. Former Astros general manager Jeff Luhnow also was suspended for the season, and later fired for his role.
Hinch has admitted knowledge about the scheme, but Luhnow has denied involvement.
In five seasons with the Astros, Hinch posted a 481-329 managerial record. He went 89-123 in two seasons with the Arizona Diamondbacks before he joined Houston in 2015. He led the Astros to a World Series in 2017, the season when the team stole opponents' signs, and another American League pennant in 2019.
Gardenhire, 63, posted a 132-241 record in three seasons with the Tigers. He had a 1,067-1,039 record in 13 seasons with the Minnesota Twins before joining Detroit.
The Tigers went 23-35 this season and failed to make the playoffs.