The Scottish giants have endured a horrendous group-stage campaign this season and they sit rock bottom of Group A after losing all of their first five games, including a 4-0 defeat away at Ajax in matchday one.
Rangers have also lost twice by a 3-0 scoreline against group leaders Napoli, while Liverpool followed up a 2-0 win over the Gers at Anfield with a 7-1 thrashing at Ibrox.
Scott Arfield's opening goal in the home defeat to the Merseysiders is the only time Rangers have found the back of the net in Group A, with 19 goals conceded at the other end across the five matches.
Giovanni van Bronckhorst's side are one of only four teams in this season's competition, along with Old Firm rivals Celtic, Copenhagen and Viktoria Plzen, who are yet to win in the group stage.
However, the Gers are at risk of making unwanted Champions League history as they could record the worst ever group-stage performance if they suffer another defeat against Ajax.
The worst ever group-stage performance was carried out by Croatian outfit Dinamo Zagreb in 2011-12 when they failed to pick up a single point and ended with a goal difference of -19, scoring three times and conceding 22.
Rangers currently see their goal difference at -18 after five matches, but they are not the only side seeking to avoid this record, as Viktoria Plzen possess a goal difference of -17 (three goals scored and 20 conceded) after five straight group-stage defeats this term.
Plzen have at least been given a glimmer of hope to secure something from their final Group C clash against La Liga giants Barcelona, who are set to rest a number of first-team stars as they are guaranteed to finish third and drop down into the Europa League.
Rangers will equal Zagreb's worst ever group-stage performance if they lose by a one-goal margin on Tuesday, but a defeat by two or more goals could see the Glaswegian giants take the unwanted title away from the Croatian side if Plzen avoid a heavy defeat against Barca.
Van Bronckhorst's men could also become the first Scottish team to lose all six European Cup/Champions League group fixtures if they fail to avoid defeat against Ajax.
Claiming at least a draw against Ajax could prove challenging for Rangers, who have lost all five previous meetings against the Dutch outfit in European competition.
Ajax themselves have endured a difficult group-stage campaign so far this season and they head to Ibrox off the back of four straight Group A defeats, including a 3-0 home loss to Liverpool last week.
It is still mathematically possible for Rangers to leapfrog Ajax into third place and drop down into the Europa League, but they will need to beat the perennial Eredivisie champions by a five-goal margin on Tuesday.