The Scotland international is yet to settle personal terms but the Canaries have made a swift move to sign him.
Norwich have shipped 15 goals in their opening seven games in all competitions as they struggle under new boss Daniel Farke.
They lost 4-0 at newly promoted Millwall on Saturday which underlined the need for defensive reinforcements.
The Canaries have rebuilt their defence this summer but still desperately need to add quality to their backline as they sit in the Sky Bet Championship bottom three.
Hanley is surplus to requirements at Newcastle with Fulham also reportedly interested.