The Baggies have been searching for a new manager since the departure of Roy Hodgson, who was named the new England manager in May.
Rangnick was thought to be the favourite for the role, but his adviser Oliver Mintzlaff has stated that he turned down the role.
"After careful consideration, Ralf Rangnick has decided to decline the offer presented to him by Premier League club West Bromwich Albion," Mintzlaff told Spox.
|BAGGIES TO LOSE THEIR BOING?
|West Brom are 9/2 with Paddy Power to be relegated from the Premier League next season.|
The 53-year-old has managed at eight clubs including VfB Stuttgart and Hannover 96, and was most recently in charge at Schalke until he quit due to exhaustion. Since then, the German has been linked closely with taking over at Turkish side Besiktas.
West Brom are reportedly set to confirm ex-Liverpool assistant coach Steve Clarke as their new first team manager. Clarke has had previous experience as an assistant at Chelsea, West Ham and last season at Anfield alongside Kenny Dalglish.
Under Hodgson West Brom finished 10th in the league and the club are believed to be close to announcing his replacement.