City ended a 44-year title drought in the English league last season while Dortmund successfully defended its Bundesliga title. However, both domestic champions were eliminated from Europe's top club competition in the group phase.
And while Dortmund beat Ajax 1-0 in their opener two weeks ago, City has very little room left for error in what is considered the tournament's toughest group after losing 3-2 at Real Madrid.
In the other Group D match on Wednesday, Madrid visits Ajax.
If City falls to Dortmund and Madrid wins in Amsterdam, the English club would find itself six points out of the running for one of the top two spots to the knockout round.
"I think it's going to be a tough, massive game tomorrow," City midfielder Yaya Toure said. "We'll need to improve on our performance in Madrid and work really hard as Dortmund are a fantastic team. They all defend together and attack together.
"But we need a good result for our fans. We know we want to do it and we can do it. We're already in a delicate position, but we've got our first game at home and we want to show the fans we can make up for the mistakes we made in Madrid and get a good result tomorrow."
The match at Etihad Stadium will pit Manchester City's star-studded front led by Toure and forward David Silva against a Dortmund attack renowned for its speed that is coming off a 5-0 rout of Borussia Moenchengladbach on Saturday.
"The confidence is back," Dortmund midfielder Jakub Blaszczykowski said after Saturday's win. "(Manchester City) has a really strong team. But we also have a lot of quality in our ranks."
Dortmund is hoping to make a bigger impact in the Champions League after finishing bottom of its group on its return to the competition last season. To do so, the team will have to break City's run of 17 home matches without a loss in European competition.
Dortmund striker Robert Lewandowski was rested on Saturday and should start.
Former champions Madrid and Ajax are meeting for the third straight season, with Madrid looking to extend its recent dominance over the Dutch team.
The Spanish champions have eliminated Ajax from the group phase the last two seasons, winning all four meetings by an aggregate score of 12-0.
After its sloppy start in Spain, Madrid finally strung together back-to-back wins for the first time this season by thrashing Deportivo La Coruna 5-1 - with a hat trick from Cristiano Ronaldo.
Madrid visits Barcelona on Sunday and does not want to be distracted by the always important "clasico" match.
"Now we are playing in the Champions League. We have to be focused and later think about Barcelona," Madrid defender Pepe said. "Our group is the most difficult, but we have a talented squad and we are going out to win."
Ajax striker Ryan Babel said the fact that Madrid coach Jose Mourinho was in Amsterdam on Saturday to watch Ajax beat league leader FC Twente 1-0 showed he is taking the match at the Amsterdam Arena seriously.
"Real Madrid has beaten Ajax in the last two seasons and those four victories could lead to them underestimating us," Babel said. "But Mourinho will have seen against Twente that we have made great strides."