The Turkish champions face tough tests against Real Madrid and Juventus in Group B but the Italian coach believes his players have what it takes to progress
The Turkish champions currently sit second in Group B but they are level on points with third-placed Copenhagen, and just one ahead of Juventus.
However, while they next face a daunting trip to the Santiago Bernabeu before hosting the Bianconeri in their final pool game, Mancini is upbeat about his side's hopes of reaching the last 16.
"Galatasaray are a very good team who have the potential to do well this season," the Italian coach told Uefa.com.
"It's never easy in the Champions League and our group is particularly tough. However, we can progress.
"I'm still confident of qualifying. We need to improve as a team but I am hopeful of a good result in our next game against Real Madrid.
"Then we will have everything to play for. As they say in football, never say never."
Mancini only took charge of Gala at the tail end of September, following the departure of Fatih Terim for the Turkish national team.