It is understood that Rohl was interviewed last week and was eager to get to work in time for this Saturday’s Scottish Premiership match against Dundee United.
However, he now feels that the timing is not right for him to continue in the process and has reluctantly informed Rangers that he no longer wishes to be considered for the vacancy.
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Rohl’s withdrawal leaves Kevin Muscat as the main contender to take over in Govan. His appointment may not be entirely simple, though.
Indeed, Rangers would have to pay his current club, Shanghai Port, a seven-figure compensation fee to complete a deal.
On top of that, Muscat is expected to remain in charge of Shanghai until they wrap up the Chinese Super League title.
No agreement has been finalised on personal terms or those with Shanghai to secure a move.
Steven Smith, the head coach of Rangers’ under-19s, has been leading first-team training alongside Brian Gilmour of late. Smith could yet take charge of this weekend’s match against United.