However, there are grounds for optimism for Thomas Tuchel's men ahead of the encounter. bundesliga.com outlines five good reasons why Dortmund can still go through to the semi-finals...
1) The Aubameyeng factor
Seventeen other teams at home and abroad have found the Gabon captain impossible to contain this season, however, and his 33 goals in all competitions would strike fear into the hearts of the hardiest of defences.
Monaco's first-choice centre-backs Jemerson and Kamil Glik are fine competitors but they are not blessed with particular pace. Aubameyang has been clocked covering 30 metres in 3.7 seconds and he rarely goes twice without scoring in a tie.
The 27-year-old could also feel he has a point to prove, having netted only two goals in 23 appearances while on loan at Monaco in the 2010/2011 season.
2) The Yellow Wall on tour
At home, Dortmund have the backing of some of the best supporters in the world – most notably the diehards that make up the Südtribune’s famous Yellow Wall at Signal Iduna Park.
That standing-only terrace alone has a bigger capacity (almost 25,000) than Monaco’s Stade Louis II, so the travelling support will have a major role to play in the principality on Wednesday.
Despite being top of the table, Monaco have the lowest average attendance of any team in France’s Ligue 1 this season – a little over 9,000. There could be a capacity crowd of 18,000 for a Champions League quarter-final second-leg but with the visiting Dortmund fans set to make their customary racket, then the home side might start to feel the pressure if and when things get tight.
3) Rolls Reus returns
They like eye-catching, top-of-the-range products in Monaco so the locals will presumably appreciate the sight of Marco Reus rolling into town. The German ace made a goalscoring comeback from injury in the weekend win over Eintracht Frankfurt and he is certain to offer Dortmund a greater threat in the second leg.
An out-of-position centre back Andrea Raggi manned the left-back position for Monaco in the first leg but – despite making the second goal – their first-choice Benjamin Mendy is expected to return, and he is much more comfortable overlapping. That could mean the kind of space in behind that Reus and teenage wing wizard Dembele thrive on.
4) Doing it for Bartra
The players will also be desperate to do it for a man who will not be on the pitch with them. Marc Bartra was injured in the shocking attack on the team bus before last Wednesday's first leg, but is targeting a return to action within a month after undergoing surgery on his wrist.
From now until the Spanish defender’s return, his team-mates will be motivated by the thought of winning games for him. That can mean pushing themselves to the limit and surprising a few people along the way. If Greek centre back Sokratis can finish off a mazy dribble with a thumping shot into the top corner – like he did against Frankfurt – then Dortmund can get past Monaco.
Watch: Highlights of Dortmund's 3-1 win over Frankfurt on Matchday 29, dedicated to Bartra
5) A history of spectacular comebacks
Dortmund are a club with a history of spectacular comebacks. In Jürgen Klopp’s first Revierderby, back in September 2008, his side scored three goals in the final 23 minutes to come back from 3-0 down.
They have previous in the Champions League as well, of course. On their run to the final in 2013, Dortmund were 2-1 down against Malaga with seconds of their quarter-final tie to play. Injury-time goals from Reus and Felipe Santana, though, saw the 1997 European champions complete a miraculous comeback.
“My assistants and I were looking at each other in shock in the dressing room, saying 'this is crazy',” then-Dortmund boss Klopp said at the time. “This is the best I've ever felt.”
Tuchel could yet be feeling something similar at the Stade Louis II on Wednesday.