West will take charge of Hartlepool for the last time in their FA Cup tie at Southend on Saturday after being made caretaker-boss following Turner's decision to join the Owls.
The new Wednesday manager has not yet confirmed the identity of his assistant, but the Sheffield Star report that West has agreed to re-join his old boss at Hillsbrough next week.
West played a key part as assistant manager alongside Turner in Hartlepool's success.