Rangnick, 53, has emerged as the clear favourite to take over from new England head coach Hodgson. But reports that the Baggies have already made a formal offer to Rangnick are premature.
He first met with Albion officials when a guest of the club for the final home Premier League game of the campaign with Arsenal on May 13. Compensation would not be an issue as Rangnick has been without a club since leaving Schalke eight months ago because of exhaustion.
He nudged ahead of Birmingham boss Chris Hughton after it emerged the Championship club were looking for around £2 million in compensation.
Blues were also prepared to turn down Albion if they approached asking for permission to speak to Hughton who would then have had to resign to force the issue.
Rangwick 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.