Rangnick has been out of work since September after stepping down from his post at Schalke because of exhaustion.
But it is understood he is ready to return to management and has impressed Albion chairman Jeremy Peace.
Rangnick had two spells at Schalke, leading them to the semi-finals of the Champions League in 2010-11, in addition to a four-year stint at Hoffenheim.
Hughton came close to landing the Baggies job 15 months ago after the sacking of Roberto Di Matteo, only for Roy Hodgson to eventually be appointed.
Now Birmingham's compensation demands appear to have ended Hughton's chances of moving to the Hawthorns if he harboured any ambitions in that direction.
They are determined to drive a hard bargain after losing the services of Alex McLeish to Aston Villa 12 month ago.
Albion also held two rounds of talks with former Chelsea boss Claudio Ranieri - but he is now expected to move to Monaco.
With Ray Wilkins no longer in serious contention, it would appear the path is clear for Rangnick.