A deal is expected soon, league sources told ESPN's Adrian Wojnarowski on Sunday.
The 37-year-old Winger is an assistant general manager/team counsel for the Thunder. He would report directly to Lawrence Frank, the Clippers' new president of basketball operations.
Winger has spent the past seven years with Oklahoma City, working alongside executive vice president and GM Sam Presti.
The Clippers restructured their front office this offseason after Rivers relinquished his basketball operations duties and Frank was promoted. Frank is a two-time head coach with the New Jersey (now Brooklyn) Nets and the Detroit Pistons.