Los Blancos suffered a shock 3-2 home defeat to Shakhtar Donetsk in their competition opener last week, while Gladbach started their Group B challenge with a 2-2 draw away to Inter Milan.
Gladbach will head into Tuesday's European contest off the back of a 3-2 win over Mainz 05 in the Bundesliga on Saturday, with the result moving them onto eight points and leaving them fifth in the table.
Marco Rose's side also made a very encouraging start to their Champions League Group B campaign last week, picking up a point away to Inter, who needed a last-minute Romelu Lukaku effort to avoid defeat.
Gladbach have never qualified for the knockout round of this competition, with their two previous participations ending in the group stages. They also failed to qualify for the last-32 stage of the 2019-20 Europa League, finishing third in their section behind Istanbul Basaksehir and Roma.
Not since the third round of the 1985-86 UEFA Cup have the German outfit faced Madrid in European competition, but they did take on Barcelona in the group stages of the 2016-17 Champions League, losing home and away to the La Liga giants, including a 2-1 defeat on home soil.
The Colts will have been encouraged by their performance at San Siro on October 21, though, and another positive result on Tuesday would lead them nicely into their next European game with Shakhtar.
For all of the criticism aimed at the reigning Spanish champions, they are currently top of the table, picking up 13 points from their first six domestic matches of the 2020-21 campaign.
Zinedine Zidane's side were incredibly beaten by a coronavirus-hit Shakhtar in their Champions League opener last week, though, with the Ukrainian side recording a 3-2 victory at the Bernabeu.
Madrid have now lost each of their last three European matches, having also been beaten twice by Manchester City in the last-16 stage of the 2019-20 competition.
The Spanish champions have qualified for the knockout round of the Champions League in each of their 25 participations, while they are 13-time champions. Zidane's team have now lost in the round of 16 in the last two seasons, though, and will be desperate to make an impression this term.
Borussia Monchengladbach Champions League form: LWDDLD
Borussia Monchengladbach form (all competitions): LDWDDW
Real Madrid Champions League form: WDWLLL
Real Madrid form (all competitions): WWWLLW
Valentino Lazaro is back in training after recovering from a calf problem, but the on-loan Inter attacker has not played since the end of August due to a calf problem.
As for Madrid, the big news surrounds Eden Hazard, who has been named in the travelling party for the contest despite recently being on the sidelines with a muscular problem. The Belgian was not expected to return until the end of next month but could now feature against Gladbach.
Dani Carvajal, Martin Odegaard, Mariano Diaz and Alvaro Odriozola have all been left out of the squad, while Nacho has also not been included due to the knock that he picked up against Barca, meaning that Lucas Vazquez is expected to start at right-back.
Zidane is expected to stick with the majority of the XI that started against Barca, meaning that Modric might have to accept a spot on the bench once again, with Federico Valverde continuing in midfield.
The Madrid boss could potentially rest players in next weekend's league game with Huesca, but the importance of Tuesday's contest means that the likes of Karim Benzema, Casemiro, Ramos and Raphael Varane should all be in the starting XI.
Borussia Monchengladbach possible starting lineup:
Sommer; Lainer, Ginter, Elvedi, Bensebaini; Kramer, Neuhaus; Hofmann, Embolo, Thuram; Plea
Real Madrid possible starting lineup:
Courtois; Vazquez, Varane, Ramos, Mendy; Valverde, Casemiro, Kroos; Vinicius, Benzema, Asensio
We say: Borussia Monchengladbach 1-2 Real Madrid
This has all of the makings of a very interesting game at Borussia-Park. Both sides will enter the match off the back of strong domestic victories, but the pressure is certainly on Madrid after a poor result against Shakhtar. We are expecting a close game in Germany but fancy Zidane's side to claim all three points.