Sources told ESPN.com that the Thunder are nearing a deal with Griffin to fill the void on the bench created by Monty Williams' departure.
Donovan announced last week after the Thunder's elimination from the playoffs that Williams, following the death of his wife in a February car accident, would not be able to continue with the club in his coaching role next season due to family reasons.
Griffin served as an assistant coach on Scott Skiles' staff in Orlando last season and was strongly considered by the Magic as a successor to Skiles before they hired former Indiana Pacers coach Frank Vogel.
The defensive-minded Griffin, who counts Skiles and Minnesota Timberwolves coach Tom Thibodeau among his strongest coaching influences, also has a brief history with the Thunder organization after playing alongside then-rookie Kevin Durant for the last two months of the club's final season in Seattle in 2007-08. Griffin played for five teams in a nine-year NBA career.
The possibility remains that Williams will serve as an assistant coach on Mike Krzyzewski's staff for USA Basketball at the Summer Olympics in Rio as scheduled.