Neuer received praise for his display in the tense 2-1 victory over Algeria in the previous round, and Brehme believes that the Bayern Munich goalkeeper may once again have to play a key role if Germany are to edge past France in the Maracana.
"If our team can improve, which I really hope and expect they will do, it'll be a very evenly-balanced match," the 53-year-old, who scored the winner against Argentina in the 1990 World Cup final, told FIFA.com. "Both teams have got fantastic players with great quality.
"At the end of the day, maybe a world-class player like Manuel Neuer will be the deciding factor. The way he played against Algeria was incredible. In my opinion, he's been one of the players of the tournament so far."
Neuer has conceded three goals in his four appearances in Brazil this summer.