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A new manager is required after Mark Warburton exited this month.
And they suffered a 2-1 defeat by Dundee on Sunday in Graeme Murty's second game in caretaker charge.
Further meetings with hopeful contenders are planned in London over the next few days as they look to reshape their management structure.
Ross Wilson, Southampton's director of recruitment and scouting, is one of those who has already met with Rangers managing director Stewart Robertson with a view to taking on the new director of football post.
However, there are reportedly at least another three candidates vying for the role.
Former Rangers manager Alex McLeish has said he would find it hard to turn down a return to Ibrox should he be offered another job there.
Frank De Boer, the former Rangers defender, has admitted that he would be interested but not until the end of the season.
Aberdeen manager Derek McInnes, another former Rangers player, could come into the Ibrox board's thinking with his current team six points ahead of the Glasgow outfit in second place in the Scottish Premiership.
Former Crystal Palace boss Alan Pardew, St Johnstone manager Tommy Wright and Billy Davies, the former Rangers player who last managed Nottingham Forest, are behind McLeish in the bookmakers' odds.
Rangers are 30 points behind defending champions Celtic as the Ibrox side's city rivals lead the Premiership.
They have only won one of their last four games - a Scottish Cup win over Greenock Morton in Murty's first game in charge - and they are only five points ahead of Hearts as they chase a Europa League place.
However, PA reports that no appointment for either Ibrox position is expected this week, meaning Murty is again likely to be in charge when the Light Blues travel north to take on Inverness Caledonian Thistle on Friday night.
Rangers have held interviews as they seek a new team boss - and to fill the new role of director of football - PA Sport has reported.