Van Bronckhorst was given the sack after Rangers dropped points once more in their last league game before the World Cup break, away to St. Mirren as part of a disappointing run.
The Gers currently find themselves nine points behind rivals and defending champions Celtic, with only 15 games of the league season played so far.
Miller believes that the Rangers hierarchy must put a new manager into the hot seat at Ibrox by 27th November so that there is someone to take team training on the following morning.
The former Gers forward emphasised the need to give the new manager time with his squad out on the training pitch so as to effect any visible improvements before Rangers’ next fixture in the league.
“I think they ought to have a [new] manager by Sunday, 27th November, to take training on Monday morning”, Miller said on Clyde 1 Superscoreboard.
“You’ve got [about] a week now, you’ve got two weeks since the St. Mirren game to get this team ready for that game [against Hibernian].
“The longer this manager’s had on the training field with this group of players the better chance we’ll have of seeing improvement.”
Rangers play host to Hibernian on the 15th December when the Scottish Premiership resumes before the new year.
