Mahrez joined City in a club-record £60m move from Leicester City earlier this week, putting pen to paper on a five-year deal which will keep him at the Etihad Stadium until 2023.
City were the dominant force in English football last season, breaking numerous records on their way to the title, and Mahrez is now hopeful of helping them to carry that over to the Champions League.
"It's a club who wants to win this type of trophy. The Champions League is for big clubs and Manchester City are a big club," Mahrez told reporters at his official unveiling.
"They have everything to try to win the Champions League. It is a goal. Last season they lost in the quarter-final and I know they have the ambition to go further the next season.
"That's why I'm here, why I made the decision to come here, because I want to be part of this."
City were knocked out by Liverpool in the quarter-finals of the Champions League last season.