City, who were already safely through to the last 16, saw off Viktoria Plzen 4-2 at the Etihad Stadium on Wednesday to keep within three points of group leaders Bayern, but require a 3-0 win in Munich to finish first in their group.
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"We will try and beat Bayern Munich to the first spot in the group," Kolarov, who was given the captaincy by Pellegrini against Plzen, told City's official website.
"It was important to win tonight so we can beat them and have a chance to come first in the group so we can avoid some big, big teams.
"But even in second place we will be happy to finish there. We will see what happens in Munich."
City's four goals against Plzen on Wednesday means that they have now scored 22 from their last four games at the Etihad.
Kolarov is delighted with the way the team are playing at home but says they now need to improve on their form on the road if they are to have a successful season.
"We always want to play good football in front of our fans and score a lot of goals at home," he said.
"We have to keep doing this and try to score some more goals away.
"We have the game at home against Swansea and then a couple away. We have to try and win all of these games as December is a very important month for us."