A win over Madrid — which is already assured of topping Group C — coupled with a loss for Braga at Napoli in the other group game would lift Union above the Portuguese side into third place in the group and secure and the consolation prize of a place in the Europa League.
There's no consolation for finishing bottom of the group, where Union finds itself with just two points after failing to beat 10-man Braga in their previous game.
That 1-1 draw in new Union coach Nenad Bjelica's debut stretched the German team's winless streak to 16 games across all competitions, but Union finally ended that confidence-shattering run on Saturday in the Bundesliga with a 3-1 victory over Borussia Mönchengladbach.
Madrid, meanwhile, has won every game in the competition so far and is looking to complete a perfect group stage for the third time after 2011-12 and 2014-15.
Indeed, the contrast between the clubs could hardly be greater. Madrid, the tradition-steeped Spanish behemoth, has won the European Cup a record 14 times, while Union was only promoted to the Bundesliga for the first time in 2009 and is playing for the first time in the Champions League after an improbable fourth-place finish in Germany last season.
Many Union fans expected the team's success to continue this season, but the arrival of well-known names like Leonardo Bonucci, Robin Gosens and Kevin Volland in the off-season did not have the desired effect as Union's defensive stability crumbled and the team lost its efficiency in attack.
Coach Urs Fischer, who led the team to promotion in 2009, paid the price and was replaced by Bjelica.
Volland opened the scoring against Gladbach with a penalty — arguably the only way the home team was going to score — before little-known players Benedict Hollerbach and Mikkel Kaufmann grabbed their first Bundesliga goals to end Union's winless run.
Madrid had won its previous five games across all competitions until Real Betis fought back to draw 1-1 on Saturday.
Union will take some encouragement from knowing the visitors have little but pride to play for with top spot in Group C already assured — and from its own performance in the 1-0 loss to Madrid at the Santiago Bernabéu in September.
Jude Bellingham only scored Madrid's winner in the 94th minute. Unfortunately for Union, he'll likely be playing again.
The game will be played in Berlin's Olympiastadion, traditionally the home of Union's city rival Hertha Berlin. Union's Stadion An der Alten Försterei only holds 22,000 supporters and the club wanted to give as many as possible the chance to see its debut Champions League campaign. Tickets for Madrid's visit were sold out long in advance.