Negotiations are ongoing with the 46-year-old Dutchman who held positive initial talks with the Ibrox club’s sporting director Ross Wilson in London last weekend.
While Wilson is understood to have also held discussions with at least two other potential candidates, former Rangers midfielder van Bronckhorst is still the heavy odds-on favourite to be confirmed as successor to Steven Gerrard who quit to take charge of Aston Villa last week.
Even if a deal with van Bronckhorst is secured before Sunday, it’s not certain that he would be in the technical area at Hampden as the Scottish champions bid to claim a place in next month’s Premier Sports Cup Final.
Administrative and visa issues could limit him to a watching brief. Earlier this week, Rangers announced a four-man coaching team to take charge of their first team squad ahead of the Hibs match - B team manager David McCallum, his assistant Brian Gilmour, veteran player-coach Jermain Defoe and goalkeeping coach Colin Stewart.
The timing of any formal announcement by Rangers may also be dictated by the memorial service being held at Glasgow Cathedral on Friday for the club’s legendary former manager Walter Smith who died last month at the age of 73.
Rangers have already rescheduled a Premier Sports pre-match media conference with their captain James Tavernier, putting it back until Saturday morning.
Gerrard, meanwhile, will hold his first media conference as Aston Villa manager at 11am on Thursday morning.
While the international break afforded Rangers time to identify and recruit Gerrard’s successor, they are now facing a crucial spell of fixtures up until the winter break at the start of January.
After Sunday’s semi-final, they have a potentially decisive Europa League group stage fixture against Sparta Prague at Ibrox next Thursday night as they attempt to reach the knockout phase of the tournament for a fourth consecutive season.
Currently four points clear of Celtic at the top of the Premiership, their run of league games in the coming weeks includes trips to Hibs, Hearts and Aberdeen before the Old Firm showdown at Parkhead on January 2.