Gase, 40, went 23-26 in three seasons with the Dolphins, including to the playoffs in 2016.
Sam Darnold's development was priority No. 1, 2 and 3.
McCarthy was sacked as the Packers' head coach mid-way through the 2018 season.
Former Green Bay Packers Head Coach Mike McCarthy won't be coaching in the National Football League in 2019, according to ESPN's Rob Demvosky. It's been previously reported McCarthy that McCarthy will be picky about his next coaching job and wouldn't be averse to sitting out the season if he didn't find the flawless fit.
Kingsbury was hired Tuesday as the Arizona Cardinals' head coach.