The visitors, meanwhile, were knocked out of the Champions League after suffering a 3-0 defeat at home to Liverpool last week, but they will have high hopes of dropping down to the Europa League by finishing third in Group A.
Match preview
Rangers' first time competing in the Champions League group stage for more than a decade has not exactly gone to plan so far, with five defeats from five leaving them as one of only two teams without a single point to their name in this season's competition.
Progressing from Group A was always likely to be an incredibly uphill task as soon as the draw was made given the strength of Napoli, Liverpool and Ajax, but Giovanni van Bronckhorst would have expected more from his team having reached the Europa League final last season.
Scott Arfield's opener in their 7-1 defeat at home to Liverpool remains the only goal Rangers have scored across their five defeats, so while getting the result they need to drop down to the Europa League against Ajax appears to be an almost impossible proposition, they have plenty of pride to play for in front of a demanding Ibrox crowd.
Indeed, with Celtic moving four points clear at the top of the Scottish Premiership table by beating Livingston on Sunday, van Bronckhorst is a man under significant pressure given the downturn in results and performances so far this season, with zero points from a European campaign definitely not a record he will want to have on his managerial CV.
Likewise, Ajax would have expected to push Napoli and Liverpool much harder in terms of qualifying for the group stage, but they can have no complaints having lost all four of their matches against the Italian and English sides.
That said, the Dutch Eredivisie champions were the better side against Jurgen Klopp's side prior to Mohamed Salah breaking the deadlock against the run of play shortly before half-time at the Amsterdam Arena last week, with Alfred Schreuder left ruing several missed opportunities from his side.
Beating the 2018-19 champions would have meant heading to Scotland with a chance of overtaking the Reds into second spot in the group, but goals from Darwin Nunez and Harvey Elliott in the second half means Ajax will have to settle for a spot in the Europa League instead, providing they are not thrashed by Rangers having beaten them 4-0 on matchday one.
Having had a weekend off from domestic duties - where they sit above PSV Eindhoven at the summit of the Eridivisie before facing their title rivals next weekend - Schreuder will be highly confident that his team can bow out of the Champions League with a victory on Tuesday.
Rangers Champions League form:
W
L
L
L
L
L
Rangers form (all competitions):
L
W
W
D
L
W
Ajax Champions League form:
W
L
L
L
L
Ajax form (all competitions):
L
W
L
W
W
L
Team News
Rangers have a whole host of injury concerns at present, with Kemar Roofe, Glen Kamara, Ryan Jack, Connor Goldson, John Souttar, Tom Lawrence, Filip Helander and Nnamdi Ofoborh all doubtful for Tuesday's tie.
John Lundstram is suspended, too, having received his third booking in five matches against Napoli last week, leaving van Bronckhorst incredibly short of options for what essentially represents a dead rubber unless his team can pull off an unthinkable result.
Ajax, on the other hand, have almost a clean bill of health ahead of their trip to Scotland, with only Ahmetcan Kaplan missing out due to a knee injury.
Edson Alvarez and Jurrien Timber could be rested with both players only one caution away from incurring a European suspension, with Owen Wijndal and Florian Grillitsch potentially replacing them among other possible changes ahead of a huge league game against PSV at the weekend.
Rangers possible starting lineup:
McGregor; Tavernier, King, Davies, Barisic; Sands, Davis; Sakala, Arfield, Kent; Colak
Ajax possible starting lineup:
Pasveer; Rensch, Bassey, Blind, Wijndal; Klaasen, Grillitsch, Taylor; Berghuis, Kudus, Ocampos
We say: Rangers 1-1 Ajax
With Ajax likely to rest a few key players given their strong position in terms of holding onto third spot in Group A, we can envisage Rangers salvaging some pride with a positive result on Tuesday.
It is incredibly unlikely to be the manner of victory they would need in order to drop down to the Europa League rather than crashing out of Europe, but it would at least ensure that they avoid ending their involvement in the Champions League without a point to their name.